Journal of Functional Analysis最新文献

{"title":"Connection Laplacian on discrete tori with converging property","authors":"Yong Lin,&nbsp;Shi Wan,&nbsp;Haohang Zhang","doi":"10.1016/j.jfa.2025.110984","DOIUrl":"10.1016/j.jfa.2025.110984","url":null,"abstract":"<div><div>This paper presents a comprehensive analysis of the spectral properties of the connection Laplacian for both real and discrete tori. We introduce novel methods to examine these eigenvalues by employing parallel orthonormal basis in the pullback bundle on universal covering spaces. Our main results reveal that the eigenvalues of the connection Laplacian on a real torus can be expressed in terms of standard Laplacian eigenvalues, with a unique twist encapsulated in the torsion matrix. This connection is further investigated in the context of discrete tori, where we demonstrate similar results.</div><div>A significant portion of the paper is dedicated to exploring the convergence properties of a family of discrete tori towards a real torus. We extend previous findings on the spectrum of the standard Laplacian to include the connection Laplacian, revealing that the rescaled eigenvalues of discrete tori converge to those of the real torus. Furthermore, our analysis of the discrete torus occurs within a broader context, where it is not constrained to being a product of cyclic groups. Additionally, we delve into the theta functions associated with these structures, providing a detailed analysis of their behavior and convergence.</div><div>The paper culminates in a study of the regularized log-determinant of the connection Laplacian and the converging results of it. We derive formulae for both real and discrete tori, emphasizing their dependence on the spectral zeta function and theta functions.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110984"},"PeriodicalIF":1.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808226","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":"Integral Varadhan formula for non-linear heat flow","authors":"Shin-ichi Ohta ,&nbsp;Kohei Suzuki","doi":"10.1016/j.jfa.2025.110983","DOIUrl":"10.1016/j.jfa.2025.110983","url":null,"abstract":"<div><div>We prove the integral Varadhan short-time formula for non-linear heat flow on measured Finsler manifolds. To the best of the authors' knowledge, this is the first result establishing a Varadhan-type formula for non-linear semigroups. We do not assume the reversibility of the metric, thus the distance function can be asymmetric. In this generality, we reveal that the probabilistic interpretation is well-suited for our formula; the probability that a particle starting from a set <em>A</em> can be found in another set <em>B</em> describes the distance from <em>A</em> to <em>B</em>. One side of the estimates (the upper bound of the probability) is also established in the nonsmooth setting of infinitesimally strictly convex metric measure spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 110983"},"PeriodicalIF":1.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143825891","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":"Pseudo-Gevrey smoothing for the passive scalar equations near Couette","authors":"Jacob Bedrossian ,&nbsp;Siming He ,&nbsp;Sameer Iyer ,&nbsp;Fei Wang","doi":"10.1016/j.jfa.2025.110987","DOIUrl":"10.1016/j.jfa.2025.110987","url":null,"abstract":"<div><div>In this article, we study the regularity theory for two linear equations that are important in fluid dynamics: the passive scalar equation for (time-varying) shear flows close to Couette in <span><math><mi>T</mi><mo>×</mo><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> with vanishing diffusivity <span><math><mi>ν</mi><mo>→</mo><mn>0</mn></math></span> and the Poisson equation with right-hand side behaving in similar function spaces to such a passive scalar. The primary motivation for this work is to develop some of the main technical tools required for our treatment of the (nonlinear) 2D Navier-Stokes equations, carried out in our companion work. Both equations are studied with homogeneous Dirichlet conditions (the analogue of a Navier slip-type boundary condition) and the initial condition is taken to be compactly supported away from the walls. We develop smoothing estimates with the following three features:<ul><li><span>(1)</span><span><div>Uniform-in-<em>ν</em> regularity is with respect to <span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow></msub></math></span> and a time-dependent adapted vector-field Γ which approximately commutes with the passive scalar equation (as opposed to ‘flat’ derivatives), and a scaled gradient <span><math><msqrt><mrow><mi>ν</mi></mrow></msqrt><mi>∇</mi></math></span>;</div></span></li><li><span>(2)</span><span><div><span><math><mo>(</mo><msub><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow></msub><mo>,</mo><mi>Γ</mi><mo>)</mo></math></span>-regularity estimates are performed in Gevrey spaces with regularity that depends on the spatial coordinate, <em>y</em> (what we refer to as ‘pseudo-Gevrey’);</div></span></li><li><span>(3)</span><span><div>The regularity of these pseudo-Gevrey spaces degenerates to finite regularity near the center of the channel and hence standard Gevrey product rules and other amenable properties do not hold.</div></span></li></ul> Nonlinear analysis in such a delicate functional setting is one of the key ingredients to our companion paper, <span><span>[5]</span></span>, which proves the full nonlinear asymptotic stability of the Couette flow with slip boundary conditions. The present article introduces new estimates for the associated linear problems in these degenerate pseudo-Gevrey spaces, which is of independent interest.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 110987"},"PeriodicalIF":1.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808609","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":"Inverse problems for a quasilinear hyperbolic equation with multiple unknowns","authors":"Yan Jiang ,&nbsp;Hongyu Liu ,&nbsp;Tianhao Ni ,&nbsp;Kai Zhang","doi":"10.1016/j.jfa.2025.110986","DOIUrl":"10.1016/j.jfa.2025.110986","url":null,"abstract":"<div><div>We propose and study several inverse boundary problems associated with a quasilinear hyperbolic equation of the form <span><math><mi>c</mi><msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><msubsup><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mi>u</mi><mo>=</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>+</mo><mi>F</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo><mo>)</mo><mo>+</mo><mi>G</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></span> on a compact Riemannian manifold <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> with boundary. We show that if <span><math><mi>F</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></span> is monomial and <span><math><mi>G</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></span> is analytic in <em>u</em>, then <span><math><mi>F</mi><mo>,</mo><mi>G</mi></math></span> and <em>c</em> as well as the associated initial data can be uniquely determined and reconstructed by the corresponding hyperbolic DtN (Dirichlet-to-Neumann) map. Our work leverages the construction of proper Gaussian beam solutions for quasilinear hyperbolic PDEs as well as their intriguing applications in conjunction with light-ray transforms and stationary phase techniques for related inverse problems. The results obtained are also of practical importance in assorted applications with nonlinear waves.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 110986"},"PeriodicalIF":1.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808582","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":"Tracial central states on compact quantum groups","authors":"Amaury Freslon ,&nbsp;Adam Skalski ,&nbsp;Simeng Wang","doi":"10.1016/j.jfa.2025.110988","DOIUrl":"10.1016/j.jfa.2025.110988","url":null,"abstract":"<div><div>Motivated by classical investigation of conjugation invariant positive-definite functions on discrete groups, we study <em>tracial central states</em> on universal C*-algebras associated with compact quantum groups, where centrality is understood in the sense of invariance under the adjoint action. We fully classify such states on <em>q</em>-deformations of compact Lie groups, on free orthogonal quantum groups, quantum permutation groups and on quantum hyperoctahedral groups.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 110988"},"PeriodicalIF":1.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815320","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":"Functional calculus on weighted Sobolev spaces for the Laplacian on the half-space","authors":"Nick Lindemulder ,&nbsp;Emiel Lorist ,&nbsp;Floris B. Roodenburg ,&nbsp;Mark C. Veraar","doi":"10.1016/j.jfa.2025.110985","DOIUrl":"10.1016/j.jfa.2025.110985","url":null,"abstract":"<div><div>In this paper, we consider the Laplace operator on the half-space with Dirichlet and Neumann boundary conditions. We prove that this operator admits a bounded <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-calculus on Sobolev spaces with power weights measuring the distance to the boundary. These weights do not necessarily belong to the class of Muckenhoupt <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> weights.</div><div>We additionally study the corresponding Dirichlet and Neumann heat semigroup. It is shown that these semigroups, in contrast to the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-case, have polynomial growth. Moreover, maximal regularity results for the heat equation are derived on inhomogeneous and homogeneous weighted Sobolev spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 110985"},"PeriodicalIF":1.7,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143833916","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":"Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy","authors":"Matthias Erbar ,&nbsp;Martin Huesmann ,&nbsp;Jonas Jalowy ,&nbsp;Bastian Müller","doi":"10.1016/j.jfa.2025.110974","DOIUrl":"10.1016/j.jfa.2025.110974","url":null,"abstract":"<div><div>We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation between two stationary random measures along a shortest curve connecting them. In the setting of stationary point processes we leverage this transport distance to give a geometric interpretation for the evolution of infinite particle systems with stationary distribution. Namely, we characterise the evolution of infinitely many Brownian motions as the gradient flow of the specific relative entropy w.r.t. the Poisson point process. Further, we establish displacement convexity of the specific relative entropy along optimal interpolations of point processes and establish a stationary analogue of the HWI inequality, relating specific entropy, transport distance, and a specific relative Fisher information.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110974"},"PeriodicalIF":1.7,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808224","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":"Generic density of equivariant min-max hypersurfaces","authors":"Tongrui Wang","doi":"10.1016/j.jfa.2025.110979","DOIUrl":"10.1016/j.jfa.2025.110979","url":null,"abstract":"<div><div>For a compact Riemannian manifold <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> acted isometrically on by a compact Lie group <em>G</em> with cohomogeneity <span><math><mrow><mi>Cohom</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mn>2</mn></math></span>, we show the Weyl asymptotic law for the <em>G</em>-equivariant volume spectrum. As an application, we show in the <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>G</mi></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span>-generic sense with a certain dimension assumption that the union of min-max minimal <em>G</em>-hypersurfaces (with free boundary) is dense in <em>M</em>, whose boundaries' union is also dense in ∂<em>M</em>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110979"},"PeriodicalIF":1.7,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799922","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":"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}