Pub Date : 2024-10-23DOI: 10.1016/j.jfa.2024.110711
Weiwei Ding , Xiao Li , Xing Liang
This paper is devoted to studying the existence of traveling wave solutions for reaction-diffusion equations with fractional Laplacians in time-periodic environments. By developing a dynamical systems approach, we establish the existence of propagating terraces for equations with multistable nonlinearities, which consequently implies the existence of bistable traveling waves. Furthermore, we investigate whether traveling waves exist in the multistable case. We provide an affirmative answer to this question for a special type of nonlinearity in high-frequency oscillating environments, and determine the homogenized limit of the traveling waves as the period approaches 0.
{"title":"Time-periodic traveling waves and propagating terraces for multistable equations with a fractional Laplacian: An abstract dynamical systems approach","authors":"Weiwei Ding , Xiao Li , Xing Liang","doi":"10.1016/j.jfa.2024.110711","DOIUrl":"10.1016/j.jfa.2024.110711","url":null,"abstract":"<div><div>This paper is devoted to studying the existence of traveling wave solutions for reaction-diffusion equations with fractional Laplacians in time-periodic environments. By developing a dynamical systems approach, we establish the existence of propagating terraces for equations with multistable nonlinearities, which consequently implies the existence of bistable traveling waves. Furthermore, we investigate whether traveling waves exist in the multistable case. We provide an affirmative answer to this question for a special type of nonlinearity in high-frequency oscillating environments, and determine the homogenized limit of the traveling waves as the period approaches 0.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 2","pages":"Article 110711"},"PeriodicalIF":1.7,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554210","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}
Pub Date : 2024-10-23DOI: 10.1016/j.jfa.2024.110722
Julián Haddad , Dylan Langharst , Eli Putterman , Michael Roysdon , Deping Ye
Schneider introduced an inter-dimensional difference body operator on convex bodies, and proved an associated inequality. In the prequel to this work, we showed that this concept can be extended to a rich class of operators from convex geometry and proved the associated isoperimetric inequalities. The role of cosine-like operators, which generate convex bodies in from those in , were replaced by inter-dimensional simplicial operators, which generate convex bodies in from those in (or vice versa). In this work, we treat the extensions of these operators, and, furthermore, extend the role of the simplex to arbitrary m-dimensional convex bodies containing the origin. We establish mth-order isoperimetric inequalities, including the mth-order versions of the Petty projection inequality, Busemann-Petty centroid inequality, Santaló inequalities, and affine Sobolev inequalities. As an application, we obtain isoperimetric inequalities for the volume of the operator norm of linear functionals .
{"title":"Higher-order Lp isoperimetric and Sobolev inequalities","authors":"Julián Haddad , Dylan Langharst , Eli Putterman , Michael Roysdon , Deping Ye","doi":"10.1016/j.jfa.2024.110722","DOIUrl":"10.1016/j.jfa.2024.110722","url":null,"abstract":"<div><div>Schneider introduced an inter-dimensional difference body operator on convex bodies, and proved an associated inequality. In the prequel to this work, we showed that this concept can be extended to a rich class of operators from convex geometry and proved the associated isoperimetric inequalities. The role of cosine-like operators, which generate convex bodies in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> from those in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, were replaced by inter-dimensional simplicial operators, which generate convex bodies in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mi>m</mi></mrow></msup></math></span> from those in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> (or vice versa). In this work, we treat the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> extensions of these operators, and, furthermore, extend the role of the simplex to arbitrary <em>m</em>-dimensional convex bodies containing the origin. We establish <em>m</em>th-order <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> isoperimetric inequalities, including the <em>m</em>th-order versions of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> Petty projection inequality, <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> Busemann-Petty centroid inequality, <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> Santaló inequalities, and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> affine Sobolev inequalities. As an application, we obtain isoperimetric inequalities for the volume of the operator norm of linear functionals <span><math><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><msub><mrow><mo>‖</mo><mo>⋅</mo><mo>‖</mo></mrow><mrow><mi>E</mi></mrow></msub><mo>)</mo><mo>→</mo><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>,</mo><msub><mrow><mo>‖</mo><mo>⋅</mo><mo>‖</mo></mrow><mrow><mi>F</mi></mrow></msub><mo>)</mo></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 2","pages":"Article 110722"},"PeriodicalIF":1.7,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554256","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}
We introduce the notion of BMT independence, enabling the study of arbitrary mixtures of Boolean, monotone, and tensor independence and generalizing the notion of BM independence of J. Wysoczanski. pairwise independence relations are encoded through a directed graph, which in turn determines the way mixed moments must be computed. Corresponding Central and Poisson-Type Limit Theorems are provided along with an explicit construction to realize BMT independent random variables as bounded operators on the tensor product of Hilbert spaces.
我们引入了 BMT 独立性概念，从而能够研究布尔、单调和张量独立性的任意混合，并推广了 J. Wysoczanski 的 BM 独立性概念。我们还提供了相应的中心极限定理和泊松型极限定理，以及实现 BMT 独立随机变量作为希尔伯特空间张量乘上有界算子的明确构造。
{"title":"BMT independence","authors":"Octavio Arizmendi , Saul Rogelio Mendoza , Josue Vazquez-Becerra","doi":"10.1016/j.jfa.2024.110712","DOIUrl":"10.1016/j.jfa.2024.110712","url":null,"abstract":"<div><div>We introduce the notion of BMT independence, enabling the study of arbitrary mixtures of Boolean, monotone, and tensor independence and generalizing the notion of BM independence of J. Wysoczanski. pairwise independence relations are encoded through a directed graph, which in turn determines the way mixed moments must be computed. Corresponding Central and Poisson-Type Limit Theorems are provided along with an explicit construction to realize BMT independent random variables as bounded operators on the tensor product of Hilbert spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 2","pages":"Article 110712"},"PeriodicalIF":1.7,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594152","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}
Pub Date : 2024-10-23DOI: 10.1016/j.jfa.2024.110709
Guoyi Xu
For a geodesic ball with non-negative Ricci curvature and mean convex boundary, it is known that the first Dirichlet eigenvalue of this geodesic ball has a sharp lower bound in term of its radius. We show a quantitative explicit inequality, which bounds the width of geodesic ball in terms of the spectral gap between the first Dirichlet eigenvalue and the corresponding sharp lower bound.
{"title":"The first Dirichlet eigenvalue and the width","authors":"Guoyi Xu","doi":"10.1016/j.jfa.2024.110709","DOIUrl":"10.1016/j.jfa.2024.110709","url":null,"abstract":"<div><div>For a geodesic ball with non-negative Ricci curvature and mean convex boundary, it is known that the first Dirichlet eigenvalue of this geodesic ball has a sharp lower bound in term of its radius. We show a quantitative explicit inequality, which bounds the width of geodesic ball in terms of the spectral gap between the first Dirichlet eigenvalue and the corresponding sharp lower bound.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 2","pages":"Article 110709"},"PeriodicalIF":1.7,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554257","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}
Pub Date : 2024-10-23DOI: 10.1016/j.jfa.2024.110710
Marcus Waurick
The notion of nonlocal H-convergence is extended to domains with nontrivial topology, that is, domains with non-vanishing harmonic Dirichlet and/or Neumann fields. If the space of harmonic Dirichlet (or Neumann) fields is infinite-dimensional, there is an abundance of choice of pairwise incomparable topologies generalising the one for topologically trivial Ω. It will be demonstrated that if the domain satisfies the Maxwell compactness property the corresponding natural version of the corresponding (generalised) nonlocal H-convergence topology has no such ambiguity. Moreover, on multiplication operators the nonlocal H-topology coincides with the one induced by (local) H-convergence introduced by Murat and Tartar. The topology is used to obtain nonlocal homogenisation results including convergence of the associated energy for electrostatics. The derived techniques prove useful to deduce a new compactness criterion relevant for nonlinear static Maxwell problems.
非局部H收敛的概念被扩展到具有非琐碎拓扑学的域，即具有非凡谐狄利克特场和/或诺伊曼场的域。如果谐波 Dirichlet（或 Neumann）场的空间是无限维的，那么在拓扑上琐碎的 Ω 的拓扑的广义上，就有大量成对的不可比拓扑可供选择。我们将证明，如果域满足麦克斯韦紧凑性，那么相应的（广义的）非局部 H 趋同拓扑的自然版本就没有这种模糊性。此外，在乘法算子上，非局部 H 拓扑与 Murat 和 Tartar 引入的（局部）H-收敛所诱导的拓扑重合。该拓扑用于获得非局部均质化结果，包括静电相关能量的收敛。推导出的技术证明有助于推导出与非线性静态麦克斯韦问题相关的新紧凑性准则。
{"title":"Nonlocal H-convergence for topologically nontrivial domains","authors":"Marcus Waurick","doi":"10.1016/j.jfa.2024.110710","DOIUrl":"10.1016/j.jfa.2024.110710","url":null,"abstract":"<div><div>The notion of nonlocal <em>H</em>-convergence is extended to domains with nontrivial topology, that is, domains with non-vanishing harmonic Dirichlet and/or Neumann fields. If the space of harmonic Dirichlet (or Neumann) fields is infinite-dimensional, there is an abundance of choice of pairwise incomparable topologies generalising the one for topologically trivial Ω. It will be demonstrated that if the domain satisfies the Maxwell compactness property the corresponding natural version of the corresponding (generalised) nonlocal <em>H</em>-convergence topology has no such ambiguity. Moreover, on multiplication operators the nonlocal <em>H</em>-topology coincides with the one induced by (local) <em>H</em>-convergence introduced by Murat and Tartar. The topology is used to obtain nonlocal homogenisation results including convergence of the associated energy for electrostatics. The derived techniques prove useful to deduce a new compactness criterion relevant for nonlinear static Maxwell problems.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110710"},"PeriodicalIF":1.7,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551912","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}
Pub Date : 2024-10-23DOI: 10.1016/j.jfa.2024.110718
Tattwamasi Amrutam , Yair Hartman , Hanna Oppelmayer
We approach the study of sub-von Neumann algebras of the group von Neumann algebra for countable groups Γ from a dynamical perspective. It is shown that admits a maximal invariant amenable subalgebra. The notion of invariant probability measures (IRAs) on the space of subalgebras is introduced, analogous to the concept of Invariant Random Subgroups. And it is shown that amenable IRAs are supported on the maximal amenable invariant subalgebra.
我们从动力学的角度来研究可数群 Γ 的群 von Neumann 代数 L(Γ) 的子 von Neumann 代数。研究表明，L(Γ) 存在一个最大不变可变子代数。引入了子代数空间上的不变概率度量（IRAs）概念，类似于不变随机子群的概念。并证明了可变 IRA 在最大可变不变子代数上得到支持。
{"title":"On the amenable subalgebras of group von Neumann algebras","authors":"Tattwamasi Amrutam , Yair Hartman , Hanna Oppelmayer","doi":"10.1016/j.jfa.2024.110718","DOIUrl":"10.1016/j.jfa.2024.110718","url":null,"abstract":"<div><div>We approach the study of sub-von Neumann algebras of the group von Neumann algebra <span><math><mi>L</mi><mo>(</mo><mi>Γ</mi><mo>)</mo></math></span> for countable groups Γ from a dynamical perspective. It is shown that <span><math><mi>L</mi><mo>(</mo><mi>Γ</mi><mo>)</mo></math></span> admits a maximal invariant amenable subalgebra. The notion of invariant probability measures (IRAs) on the space of subalgebras is introduced, analogous to the concept of Invariant Random Subgroups. And it is shown that amenable IRAs are supported on the maximal amenable invariant subalgebra.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 2","pages":"Article 110718"},"PeriodicalIF":1.7,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554255","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}
Pub Date : 2024-10-23DOI: 10.1016/j.jfa.2024.110724
Bruno M. Braga , Gilles Lancien
We introduce a new notion of embeddability between Banach spaces. By studying the classical Mazur map, we show that it is strictly weaker than the notion of coarse embeddability. We use the techniques from metric cotype introduced by M. Mendel and A. Naor to prove results about cotype preservation and complete our study of embeddability between spaces. We confront our notion with nonlinear invariants introduced by N. Kalton, which are defined in terms of concentration properties for Lipschitz maps defined on countably branching Hamming or interlaced graphs. Finally, we address the problem of the embeddability into .
我们引入了巴拿赫空间之间可嵌入性的新概念。通过研究经典的马祖尔映射，我们证明了它比粗糙可嵌入性概念更弱。我们使用 M. Mendel 和 A. Naor 引入的度量原型技术来证明关于原型保存的结果，并完成对 ℓp 空间间可嵌入性的研究。我们将我们的概念与 N. Kalton 引入的非线性不变式相比较，后者是根据定义在可数分支汉明图或交错图上的 Lipschitz 映射的集中特性定义的。最后，我们讨论了可嵌入ℓ∞的问题。
{"title":"On the expansiveness of coarse maps between Banach spaces and geometry preservation","authors":"Bruno M. Braga , Gilles Lancien","doi":"10.1016/j.jfa.2024.110724","DOIUrl":"10.1016/j.jfa.2024.110724","url":null,"abstract":"<div><div>We introduce a new notion of embeddability between Banach spaces. By studying the classical Mazur map, we show that it is strictly weaker than the notion of coarse embeddability. We use the techniques from metric cotype introduced by M. Mendel and A. Naor to prove results about cotype preservation and complete our study of embeddability between <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> spaces. We confront our notion with nonlinear invariants introduced by N. Kalton, which are defined in terms of concentration properties for Lipschitz maps defined on countably branching Hamming or interlaced graphs. Finally, we address the problem of the embeddability into <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110724"},"PeriodicalIF":1.7,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578183","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}
Pub Date : 2024-10-22DOI: 10.1016/j.jfa.2024.110715
Julian Scheuer , Xuwen Zhang
For a function f which foliates a one-sided neighborhood of a closed hypersurface M, we give an estimate of the distance of M to a Wulff shape in terms of the -norm of the traceless F-Hessian of f, where F is the support function of the Wulff shape. This theorem is applied to prove quantitative stability results for the anisotropic Heintze-Karcher inequality, the anisotropic Alexandrov problem, as well as for the anisotropic overdetermined boundary value problem of Serrin-type.
对于使封闭超曲面 M 的单边邻域叶面化的函数 f，我们给出了 M 与 Wulff 形的距离的估计值，该估计值是以 f 的无迹 F-Hessian 的 Lp-norm 表示的，其中 F 是 Wulff 形的支持函数。该定理可用于证明各向异性海因茨-卡尔切不等式、各向异性亚历山德罗夫问题以及塞林型各向异性超定边界值问题的定量稳定性结果。
{"title":"Stability of the Wulff shape with respect to anisotropic curvature functionals","authors":"Julian Scheuer , Xuwen Zhang","doi":"10.1016/j.jfa.2024.110715","DOIUrl":"10.1016/j.jfa.2024.110715","url":null,"abstract":"<div><div>For a function <em>f</em> which foliates a one-sided neighborhood of a closed hypersurface <em>M</em>, we give an estimate of the distance of <em>M</em> to a Wulff shape in terms of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-norm of the traceless <em>F</em>-Hessian of <em>f</em>, where <em>F</em> is the support function of the Wulff shape. This theorem is applied to prove quantitative stability results for the anisotropic Heintze-Karcher inequality, the anisotropic Alexandrov problem, as well as for the anisotropic overdetermined boundary value problem of Serrin-type.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110715"},"PeriodicalIF":1.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551910","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}
Pub Date : 2024-10-22DOI: 10.1016/j.jfa.2024.110705
Fanhao Kong , Wenhao Zhao
We prove a frequency-independent bound on trigonometric functions of a class of singular Gaussian random fields, which arise naturally from weak universality problems for singular stochastic PDEs. This enables us to reduce the regularity assumption on the nonlinearity of the microscopic models (for pathwise convergence) in KPZ and dynamical in the previous works of Hairer-Xu and Furlan-Gubinelli to heuristically optimal thresholds required by PDE structures.
{"title":"A frequency-independent bound on trigonometric polynomials of Gaussians and applications","authors":"Fanhao Kong , Wenhao Zhao","doi":"10.1016/j.jfa.2024.110705","DOIUrl":"10.1016/j.jfa.2024.110705","url":null,"abstract":"<div><div>We prove a frequency-independent bound on trigonometric functions of a class of singular Gaussian random fields, which arise naturally from weak universality problems for singular stochastic PDEs. This enables us to reduce the regularity assumption on the nonlinearity of the microscopic models (for pathwise convergence) in KPZ and dynamical <span><math><msubsup><mrow><mi>Φ</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></msubsup></math></span> in the previous works of Hairer-Xu and Furlan-Gubinelli to heuristically optimal thresholds required by PDE structures.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110705"},"PeriodicalIF":1.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551913","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}
Pub Date : 2024-10-22DOI: 10.1016/j.jfa.2024.110716
Elie Abdo , Fizay-Noah Lee
We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel Gagliardo-Nirenberg type interpolation inequalities. Moreover, we use them to address the long-time dynamics of some nonlinear nonlocal drift-diffusion models and prove the exponential decay of their solutions to constant steady states.
{"title":"Logarithmic Sobolev inequalities for bounded domains and applications to drift-diffusion equations","authors":"Elie Abdo , Fizay-Noah Lee","doi":"10.1016/j.jfa.2024.110716","DOIUrl":"10.1016/j.jfa.2024.110716","url":null,"abstract":"<div><div>We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel Gagliardo-Nirenberg type interpolation inequalities. Moreover, we use them to address the long-time dynamics of some nonlinear nonlocal drift-diffusion models and prove the exponential decay of their solutions to constant steady states.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 1","pages":"Article 110716"},"PeriodicalIF":1.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553560","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}
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