Journal of Functional Analysis最新文献

{"title":"New solutions for the Lane-Emden problem in planar domains","authors":"Luca Battaglia ,&nbsp;Isabella Ianni ,&nbsp;Angela Pistoia","doi":"10.1016/j.jfa.2025.110967","DOIUrl":"10.1016/j.jfa.2025.110967","url":null,"abstract":"<div><div>We consider the Lane-Emden problem<span><span><span><math><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mspace></mspace><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>u</mi><mo>=</mo><mn>0</mn><mspace></mspace><mtext>on</mtext><mspace></mspace><mo>∂</mo><mi>Ω</mi><mo>,</mo></math></span></span></span> where <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> is a smooth bounded domain. When the exponent <em>p</em> is large, the existence and multiplicity of solutions strongly depend on the geometric properties of the domain, which also deeply affect their qualitative behavior. Remarkably, a wide variety of solutions, both positive and sign-changing, have been found when <em>p</em> is sufficiently large. In this paper, we focus on this topic and find new sign-changing solutions that exhibit an unexpected concentration phenomenon as <em>p</em> approaches +∞.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 110967"},"PeriodicalIF":1.7,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometry and analytic properties of the sliced Wasserstein space","authors":"Sangmin Park,&nbsp;Dejan Slepčev","doi":"10.1016/j.jfa.2025.110975","DOIUrl":"10.1016/j.jfa.2025.110975","url":null,"abstract":"<div><div>The sliced Wasserstein metric compares probability measures on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and machine learning, as it is easier to approximate and compute in high dimensions than the Wasserstein distance. While the geometry of the Wasserstein metric is quite well understood, and has led to important advances, very little is known about the geometry and metric properties of the sliced Wasserstein (SW) metric. Here we show that when the measures considered are “nice” (e.g. bounded above and below by positive multiples of the Lebesgue measure) then the SW metric is comparable to the (homogeneous) negative Sobolev norm <span><math><msup><mrow><mover><mrow><mi>H</mi></mrow><mrow><mo>˙</mo></mrow></mover></mrow><mrow><mo>−</mo><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>/</mo><mn>2</mn></mrow></msup></math></span>. On the other hand when the measures considered are close in the infinity transportation metric to a discrete measure, then the SW metric between them is close to a multiple of the Wasserstein metric. We characterize the tangent space of the SW space, and show that the speed of curves in the space can be described by a quadratic form, but that the SW space is not a length space. We establish a number of properties of the metric given by the minimal length of curves between measures – the SW length. Finally we highlight the consequences of these properties on the gradient flows in the SW metric.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 110975"},"PeriodicalIF":1.7,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143791892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Heintze-Karcher-type inequality for capillary hypersurfaces in a hyperbolic half-space","authors":"Yingxiang Hu ,&nbsp;Yong Wei ,&nbsp;Chao Xia ,&nbsp;Tailong Zhou","doi":"10.1016/j.jfa.2025.110970","DOIUrl":"10.1016/j.jfa.2025.110970","url":null,"abstract":"<div><div>In this paper, we establish a Heintze-Karcher-type inequality for compact embedded capillary hypersurfaces in a hyperbolic half-space. The proof is based on a geodesic normal map flow with respect to a Finsler metric of Randers-type induced by a special Zermelo's navigation data. As an application, we obtain an Alexandrov-type theorem for compact embedded capillary hypersurfaces of constant higher-order mean curvature in a hyperbolic half-space.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110970"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite time blowup and type II rate for harmonic heat flow from Riemannian manifolds","authors":"Shi-Zhong Du","doi":"10.1016/j.jfa.2025.110972","DOIUrl":"10.1016/j.jfa.2025.110972","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; be a &lt;em&gt;m&lt;/em&gt; dimensional Riemannian manifold with metric &lt;em&gt;g&lt;/em&gt; and &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; be a &lt;em&gt;n&lt;/em&gt; dimensional Riemannian sub-manifold of &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; with induced metric &lt;em&gt;h&lt;/em&gt;. In this paper, we will study the existence of finite time singularity to harmonic heat flow&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;△&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; and their formation patterns.&lt;/div&gt;&lt;div&gt;After works of Coron-Ghidaglia &lt;span&gt;&lt;span&gt;[10]&lt;/span&gt;&lt;/span&gt;, Ding &lt;span&gt;&lt;span&gt;[11]&lt;/span&gt;&lt;/span&gt; and Chen-Ding &lt;span&gt;&lt;span&gt;[5]&lt;/span&gt;&lt;/span&gt;, one knows blow-up solutions under smallness of initial energy for &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. Soon later, 2 dimensional blowup solutions were found by Chang-Ding-Ye in &lt;span&gt;&lt;span&gt;[8]&lt;/span&gt;&lt;/span&gt;. The first part of this paper is devoted to construction of new examples of finite time blow-up solutions without smallness conditions for &lt;span&gt;&lt;math&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. In fact, when considering rotational symmetric harmonic heat flow from &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; to &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, we will prove that the maximal solution blows up in finite time if &lt;span&gt;&lt;math&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϑ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, and exists for all time if &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;. This result can be regarded as a generalization of results of Chang-Ding-Ye &lt;span&gt;&lt;span&gt;[8]&lt;/span&gt;&lt;/span&gt; and Chang-Ding &lt;span&gt;&lt;span&gt;[6]&lt;/span&gt;&lt;/span&gt; to higher dimensional case, which relies on a completely different argument. The second part of the paper study the rate of blow-up solutions. When &lt;em&gt;M&lt;/em&gt; is a bounded domain in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and consider Dirichlet boundary condition on ∂&lt;em&gt;M&lt;/em&gt;, Hamilton (mentioned by Chang-Ding-Ye in &lt;span&gt;&lt;span&gt;[8]&lt;/span&gt;&lt;/span&gt;) has obtained that the blowup rate must be faster than &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;. Under a similar setting, it was later improved a","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110972"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convergence to stationary measures for the half-space log-gamma polymer","authors":"Sayan Das ,&nbsp;Christian Serio","doi":"10.1016/j.jfa.2025.110982","DOIUrl":"10.1016/j.jfa.2025.110982","url":null,"abstract":"<div><div>We consider the point-to-point half-space log-gamma polymer model in the unbound phase. We prove that the free energy increment process on the anti-diagonal path converges to the top marginal of a two-layer Markov chain with an explicit description, which can be interpreted as two random walks conditioned softly never to intersect. This limiting law is a stationary measure for the polymer on the anti-diagonal path.</div><div>The starting point of our analysis is an embedding of the free energy into the half-space log-gamma line ensemble recently constructed in <span><span>[8]</span></span>. Given the Gibbsian line ensemble structure, the main contribution of our work lies in developing a route to access and prove convergence to stationary measures via line ensemble techniques. Our argument relies on a description of the limiting behavior of two softly non-intersecting random walk bridges around their starting point, a result established in this paper that may be of independent interest.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110982"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability and instability of solitary-wave solutions for the nonlinear Klein-Gordon equation","authors":"Jing Li ,&nbsp;Yue Liu ,&nbsp;Yifei Wu ,&nbsp;Haohao Zheng","doi":"10.1016/j.jfa.2025.110981","DOIUrl":"10.1016/j.jfa.2025.110981","url":null,"abstract":"&lt;div&gt;&lt;div&gt;The nonlinear Klein-Gordon (KG) equation,&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; is shown in the present paper to possess the solitary-wave solutions in the form of &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with the parameters &lt;em&gt;ω&lt;/em&gt; and &lt;span&gt;&lt;math&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; satisfying &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. By employing a new localized virial identity combined with the coercivity and modulation argument, it is demonstrated here that there exists a critical frequency &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; such that these localized solitary waves, when considered as solutions of the initial-value problem for the nonlinear KG equation, is dynamically stable when &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and is dynamically unstable when &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; or &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/m","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110981"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143792169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lp-spectral theory for the Laplacian on forms","authors":"Nelia Charalambous ,&nbsp;Zhiqin Lu","doi":"10.1016/j.jfa.2025.110976","DOIUrl":"10.1016/j.jfa.2025.110976","url":null,"abstract":"<div><div>In this article, we find sufficient conditions on an open Riemannian manifold so that a Weyl criterion holds for the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-spectrum of the Laplacian on <em>k</em>-forms, and also prove the decomposition of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-spectrum depending on the order of the forms. We then show that the resolvent set of an operator such as the Laplacian on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> lies outside a parabola whenever the volume of the manifold has an exponential volume growth rate, removing the requirement on the manifold to be of bounded geometry. We conclude by providing a detailed description of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> spectrum of the Laplacian on <em>k</em>-forms over hyperbolic space.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110976"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143792168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Amenable actions of compact and discrete quantum groups on von Neumann algebras","authors":"K. De Commer,&nbsp;J. De Ro","doi":"10.1016/j.jfa.2025.110973","DOIUrl":"10.1016/j.jfa.2025.110973","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi></math></span> be a compact or a discrete quantum group and <span><math><mi>A</mi><mo>⊆</mo><mi>B</mi></math></span> an inclusion of <em>σ</em>-finite <span><math><mi>G</mi></math></span>-dynamical von Neumann algebras. We prove that the <span><math><mi>G</mi></math></span>-inclusion <span><math><mi>A</mi><mo>⊆</mo><mi>B</mi></math></span> is strongly equivariantly amenable if and only if it is equivariantly amenable, using techniques from the theory of non-commutative <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-spaces. In particular, if <span><math><mo>(</mo><mi>A</mi><mo>,</mo><mi>α</mi><mo>)</mo></math></span> is a <span><math><mi>G</mi></math></span>-dynamical von Neumann algebra with <em>A σ</em>-finite, the action <span><math><mi>α</mi><mo>:</mo><mi>A</mi><mo>↶</mo><mi>G</mi></math></span> is strongly (inner) amenable if and only if the action <span><math><mi>α</mi><mo>:</mo><mi>A</mi><mo>↶</mo><mi>G</mi></math></span> is (inner) amenable. This result can be seen as a dynamical generalization of Tomatsu's result on the amenability/co-amenability duality for discrete/compact quantum groups. We also provide the first explicit examples of amenable discrete quantum groups that act non-amenably on a von Neumann algebra.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110973"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Function theory on quotient domains related to the polydisc","authors":"Mainak Bhowmik ,&nbsp;Poornendu Kumar","doi":"10.1016/j.jfa.2025.110978","DOIUrl":"10.1016/j.jfa.2025.110978","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Inner functions are the backbone of holomorphic function theory. This paper studies the inner functions on quotient domains of the open unit polydisc, &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, arising from the group action of finite pseudo-reflection groups. Such quotient domains are known to be biholomorphic to the proper image &lt;span&gt;&lt;math&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; of &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; under certain polynomial maps &lt;span&gt;&lt;math&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. The main contributions of this paper are as follows:&lt;ul&gt;&lt;li&gt;&lt;span&gt;(1)&lt;/span&gt;&lt;span&gt;&lt;div&gt;We show that the closed algebra generated by inner functions on &lt;span&gt;&lt;math&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; forms a proper subalgebra of &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, the algebra of bounded holomorphic functions on &lt;span&gt;&lt;math&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;(2)&lt;/span&gt;&lt;span&gt;&lt;div&gt;The set of all rational inner functions on &lt;span&gt;&lt;math&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is shown to be dense in the norm-unit ball of &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with respect to the uniform compact-open topology, thereby proving the Carathéodory approximation result.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;(3)&lt;/span&gt;&lt;span&gt;&lt;div&gt;As an application of the Carathéodory approximation theorem, we approximate holomorphic functions on &lt;span&gt;&lt;math&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; that are continuous in the closure of &lt;span&gt;&lt;math&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; by convex combinations of rational inner functions in the &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;-norm, thereby obtaining a version of the Fisher's theorem.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;(4)&lt;/span&gt;&lt;span&gt;&lt;div&gt;Given the two approximation results above, establishing a structure for rational inner functions is essential. We have identified the structure of rational inner functions on &lt;span&gt;&lt;math&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;.&lt;","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110978"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143792170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Blow up analysis for Keller-Segel system","authors":"Hua Chen,&nbsp;Jian-Meng Li ,&nbsp;Kelei Wang","doi":"10.1016/j.jfa.2025.110968","DOIUrl":"10.1016/j.jfa.2025.110968","url":null,"abstract":"<div><div>In this paper we develop a blow up theory for the parabolic-elliptic Keller-Segel system, which can be viewed as a parabolic counterpart to the Liouville equation. This theory is applied to the study of first time singularities, ancient solutions and entire solutions, leading to a description of the blow-up limit in the first problem, and the large scale structure in the other two problems.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110968"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143800525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}