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Weinstock inequality in hyperbolic space 双曲空间中的温斯托克不等式
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-30 DOI: 10.1016/j.jfa.2025.111155
Pingxin Gu , Haizhong Li , Yao Wan
{"title":"Weinstock inequality in hyperbolic space","authors":"Pingxin Gu ,&nbsp;Haizhong Li ,&nbsp;Yao Wan","doi":"10.1016/j.jfa.2025.111155","DOIUrl":"10.1016/j.jfa.2025.111155","url":null,"abstract":"<div><div>In this paper, we establish the Weinstock inequality for the first non-zero Steklov eigenvalue on star-shaped mean convex domains in hyperbolic space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> for <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>. In particular, when the domain is convex, our result gives an affirmative answer to Open Question 4.27 in <span><span>[7]</span></span> for the hyperbolic space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> when <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 12","pages":"Article 111155"},"PeriodicalIF":1.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144780428","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}
引用次数: 0
A shape optimization problem in cylinders and related overdetermined problems 圆柱形状优化问题及相关的超定问题
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-30 DOI: 10.1016/j.jfa.2025.111157
Paolo Caldiroli , Alessandro Iacopetti , Filomena Pacella
{"title":"A shape optimization problem in cylinders and related overdetermined problems","authors":"Paolo Caldiroli ,&nbsp;Alessandro Iacopetti ,&nbsp;Filomena Pacella","doi":"10.1016/j.jfa.2025.111157","DOIUrl":"10.1016/j.jfa.2025.111157","url":null,"abstract":"<div><div>In this paper, we study a shape optimization problem for the torsional energy associated with a domain contained in an infinite cylinder, under a volume constraint. We prove that a minimizer exists for all fixed volumes and show some of its geometric and topological properties. As this issue is closely related to the question of characterizing domains in cylinders that admit solutions to an overdetermined problem, our minimization result allows us to deduce interesting consequences in that direction. In particular, we find that, for some cylinders and some volumes, the “trivial” domain given by a bounded cylinder is not the only domain where the overdetermined problem has a solution. Moreover, it is not even a minimizer, which indicates that solutions with flat level sets are not always the best candidates for optimizing the torsional energy.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 12","pages":"Article 111157"},"PeriodicalIF":1.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144771858","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}
引用次数: 0
Weak well-posedness by transport noise for a class of 2D fluid dynamics equations 一类二维流体动力学方程的输运噪声弱适定性
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-30 DOI: 10.1016/j.jfa.2025.111158
Lucio Galeati , Dejun Luo
{"title":"Weak well-posedness by transport noise for a class of 2D fluid dynamics equations","authors":"Lucio Galeati ,&nbsp;Dejun Luo","doi":"10.1016/j.jfa.2025.111158","DOIUrl":"10.1016/j.jfa.2025.111158","url":null,"abstract":"<div><div>We establish well-posedness in law for a general class of stochastic 2D fluid dynamics equations with <span><math><mo>(</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mo>∩</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></math></span>-valued vorticity and finite kinetic energy; the noise is of Kraichnan type and spatially rough, and we allow the presence of a deterministic forcing <em>f</em>. This class includes as primary examples logarithmically regularized 2D Euler and hypodissipative 2D Navier–Stokes equations. In the first case, our result solves the open problem posed by Flandoli in <span><span>[43]</span></span>. In the latter case, for well-chosen forcing <em>f</em>, the corresponding deterministic PDE without noise has recently been shown in <span><span>[3]</span></span> to be ill-posed; consequently, the addition of noise truly improves the solution theory for such PDE.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 12","pages":"Article 111158"},"PeriodicalIF":1.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144771857","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}
引用次数: 0
Uniform stability of equilibria in the inviscid limit for the Navier-Stokes-Korteweg system Navier-Stokes-Korteweg系统无粘极限平衡点的一致稳定性
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-30 DOI: 10.1016/j.jfa.2025.111156
Xueke Pu , Xiuli Xu , Jingjun Zhang
{"title":"Uniform stability of equilibria in the inviscid limit for the Navier-Stokes-Korteweg system","authors":"Xueke Pu ,&nbsp;Xiuli Xu ,&nbsp;Jingjun Zhang","doi":"10.1016/j.jfa.2025.111156","DOIUrl":"10.1016/j.jfa.2025.111156","url":null,"abstract":"<div><div>This paper considers a stability result for the three-dimensional Navier-Stokes-Korteweg system uniformly in the inviscid limit. We obtain a unique global smooth solution close to the constant equilibria <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mrow><mn>0</mn><mo>)</mo></mrow></math></span>, independent of the viscosity parameter <em>ε</em>, assuming that the potential part of the initial velocity is small independently of the viscosity parameter <em>ε</em> while the incompressible part of the initial velocity is small compared to <em>ε</em>. The proof is based on the parabolic energy estimates and dispersive properties involving the method of space time resonances.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 12","pages":"Article 111156"},"PeriodicalIF":1.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766852","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}
引用次数: 0
An extension property for noncommutative convex sets and duality for operator systems 非交换凸集的可拓性及算子系统的对偶性
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-30 DOI: 10.1016/j.jfa.2025.111153
Adam Humeniuk , Matthew Kennedy , Nicholas Manor
{"title":"An extension property for noncommutative convex sets and duality for operator systems","authors":"Adam Humeniuk ,&nbsp;Matthew Kennedy ,&nbsp;Nicholas Manor","doi":"10.1016/j.jfa.2025.111153","DOIUrl":"10.1016/j.jfa.2025.111153","url":null,"abstract":"<div><div>We characterize inclusions of compact noncommutative convex sets with the property that every continuous affine function on the smaller set can be extended to a continuous affine function on the larger set with a uniform bound. As an application of this result, we obtain a simple geometric characterization of (possibly nonunital) operator systems that are dualizable, meaning that their dual can be equipped with an operator system structure. We further establish some permanence properties of dualizability, and provide a large new class of dualizable operator systems. These results are new even when specialized to ordinary compact convex sets.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111153"},"PeriodicalIF":1.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766809","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}
引用次数: 0
A noncommutative integral on spectrally truncated spectral triples, and a link with quantum ergodicity 谱截断谱三元组上的非交换积分，以及具有量子遍历性的链路
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-30 DOI: 10.1016/j.jfa.2025.111154
Eva-Maria Hekkelman, Edward A. McDonald
{"title":"A noncommutative integral on spectrally truncated spectral triples, and a link with quantum ergodicity","authors":"Eva-Maria Hekkelman,&nbsp;Edward A. McDonald","doi":"10.1016/j.jfa.2025.111154","DOIUrl":"10.1016/j.jfa.2025.111154","url":null,"abstract":"<div><div>We propose a simple approximation of the noncommutative integral in noncommutative geometry for the Connes–Van Suijlekom paradigm of spectrally truncated spectral triples. A close connection between this approximation and the field of quantum ergodicity and work by Widom in particular immediately provides a Szegő limit formula for noncommutative geometry. We then make a connection to the density of states. Finally, we propose a definition for the ergodicity of geodesic flow for compact spectral triples. This definition is known in quantum ergodicity as uniqueness of the vacuum state for <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-dynamical systems, and for spectral triples where local Weyl laws hold this implies that the Dirac operator of the spectral triple is quantum ergodic. This brings to light a close connection between quantum ergodicity and Connes' integral formula.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 12","pages":"Article 111154"},"PeriodicalIF":1.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144780556","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}
引用次数: 0
On the existence of extensions for manifold-valued Sobolev maps on perforated domains 穿孔域上流形值Sobolev映射扩展的存在性
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111142
Chiara Gavioli , Leon Happ , Valerio Pagliari
{"title":"On the existence of extensions for manifold-valued Sobolev maps on perforated domains","authors":"Chiara Gavioli ,&nbsp;Leon Happ ,&nbsp;Valerio Pagliari","doi":"10.1016/j.jfa.2025.111142","DOIUrl":"10.1016/j.jfa.2025.111142","url":null,"abstract":"<div><div>Motivated by manifold-constrained homogenization problems, we construct suitable extensions for Sobolev functions defined on a perforated domain and taking values in a compact, connected <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-manifold without boundary. The proof combines a by now classical extension result for the unconstrained case with a retraction argument that heavily relies on the topological properties of the manifold. With the ultimate goal of providing necessary conditions for the existence of extensions for Sobolev maps between manifolds, we additionally investigate the relationship between this problem and the surjectivity of the trace operator for such functions.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111142"},"PeriodicalIF":1.6,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738067","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}
引用次数: 0
Hölder regularity of solutions of the steady Boltzmann equation with soft potentials Hölder具有软势的稳定玻尔兹曼方程解的规律性
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111146
Kung-Chien Wu , Kuan-Hsiang Wang
{"title":"Hölder regularity of solutions of the steady Boltzmann equation with soft potentials","authors":"Kung-Chien Wu ,&nbsp;Kuan-Hsiang Wang","doi":"10.1016/j.jfa.2025.111146","DOIUrl":"10.1016/j.jfa.2025.111146","url":null,"abstract":"<div><div>We consider the Hölder regularity of solutions to the steady Boltzmann equation with in-flow boundary condition in bounded and strictly convex domains <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> for gases with cutoff soft potential <span><math><mo>(</mo><mo>−</mo><mn>3</mn><mo>&lt;</mo><mi>γ</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></math></span>. We prove that there is a unique solution with a bounded <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> norm in space and velocity. This solution is Hölder continuous, and its order depends not only on the regularity of the incoming boundary data, but also on the potential power <em>γ</em>. The result for modulated soft potential case <span><math><mo>−</mo><mn>2</mn><mo>&lt;</mo><mi>γ</mi><mo>&lt;</mo><mn>0</mn></math></span> is similar to hard potential case <span><math><mo>(</mo><mn>0</mn><mo>≤</mo><mi>γ</mi><mo>&lt;</mo><mn>1</mn><mo>)</mo></math></span> since we have <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> velocity regularity from collision part. However, we observe that for very soft potential case <span><math><mo>(</mo><mo>−</mo><mn>3</mn><mo>&lt;</mo><mi>γ</mi><mo>≤</mo><mo>−</mo><mn>2</mn><mo>)</mo></math></span>, the regularity in velocity obtained by the collision part is lower (Hölder only), but the boundary regularity still can transfer to solution (in both space and velocity) by transport and collision part under the restriction of <em>γ</em>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111146"},"PeriodicalIF":1.6,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724549","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}
引用次数: 0
A refined Lusin type theorem for gradients 梯度的一个改进的Lusin型定理
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111152
Luigi De Masi, Andrea Marchese
{"title":"A refined Lusin type theorem for gradients","authors":"Luigi De Masi,&nbsp;Andrea Marchese","doi":"10.1016/j.jfa.2025.111152","DOIUrl":"10.1016/j.jfa.2025.111152","url":null,"abstract":"<div><div>We prove a refined version of the celebrated Lusin type theorem for gradients by Alberti, stating that any Borel vector field <em>f</em> coincides with the gradient of a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> function <em>g</em>, outside a set <em>E</em> of arbitrarily small Lebesgue measure. We replace the Lebesgue measure with any Radon measure <em>μ</em>, and we obtain that the estimate on the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> norm of <em>Dg</em> does not depend on <span><math><mi>μ</mi><mo>(</mo><mi>E</mi><mo>)</mo></math></span>, if the value of <em>f</em> is <em>μ</em>-a.e. orthogonal to the decomposability bundle of <em>μ</em>. We observe that our result implies the 1-dimensional version of the flat chain conjecture by Ambrosio and Kirchheim on the equivalence between metric currents and flat chains with finite mass in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> and we state a suitable generalization for <em>k</em>-forms, which would imply the validity of the conjecture in full generality.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111152"},"PeriodicalIF":1.6,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738526","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}
引用次数: 0
Carleman estimates for higher step Grushin operators 高阶Grushin算子的Carleman估计
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111150
Hendrik De Bie , Pan Lian
{"title":"Carleman estimates for higher step Grushin operators","authors":"Hendrik De Bie ,&nbsp;Pan Lian","doi":"10.1016/j.jfa.2025.111150","DOIUrl":"10.1016/j.jfa.2025.111150","url":null,"abstract":"<div><div>The higher step Grushin operators <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> are a family of sub-elliptic operators which degenerate on a sub-manifold of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mi>m</mi></mrow></msup></math></span>. This paper establishes Carleman-type inequalities for these operators. It is achieved by deriving a weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>−</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span> estimate for the Grushin-harmonic projector. The crucial ingredient in the proof is the addition formula for Gegenbauer polynomials due to T. Koornwinder and Y. Xu. As a consequence, we obtain the strong unique continuation property for the Schrödinger operators <span><math><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>+</mo><mi>V</mi></math></span> at points of the degeneracy manifold, where <em>V</em> belongs to certain <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>loc</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mi>m</mi></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111150"},"PeriodicalIF":1.6,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722808","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}
引用次数: 0
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