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Weak solutions to a hyperbolic-elliptic problem
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-12-09 DOI: 10.1016/j.jfa.2024.110798
Seonghak Kim
{"title":"Weak solutions to a hyperbolic-elliptic problem","authors":"Seonghak Kim","doi":"10.1016/j.jfa.2024.110798","DOIUrl":"10.1016/j.jfa.2024.110798","url":null,"abstract":"<div><div>We prove the existence of infinitely many local-in-time weak solutions to the initial-boundary value problem for a class of hyperbolic-elliptic equations in dimension <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span> when the range of the magnitude of the initial spatial gradient overlaps with the unstable elliptic regime. Such solutions are extracted from the method of convex integration in a Baire category setup; they are smooth outside the phase mixing zone that is determined by a modified hyperbolic evolution, continuous on the space-time domain, and Lipschitz continuous in terms of the spatial variables.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110798"},"PeriodicalIF":1.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143093264","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
Orthogonal factors of operators on the Rosenthal Xp,w spaces and the Bourgain-Rosenthal-Schechtman Rωp space
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-12-06 DOI: 10.1016/j.jfa.2024.110802
Konstantinos Konstantos , Pavlos Motakis
{"title":"Orthogonal factors of operators on the Rosenthal Xp,w spaces and the Bourgain-Rosenthal-Schechtman Rωp space","authors":"Konstantinos Konstantos ,&nbsp;Pavlos Motakis","doi":"10.1016/j.jfa.2024.110802","DOIUrl":"10.1016/j.jfa.2024.110802","url":null,"abstract":"<div><div>For <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span>, we show that the Rosenthal <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>w</mi></mrow></msub></math></span> spaces and the Bourgain-Rosenthal-Schechtman <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>ω</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span> space have the factorization property and the primary factorization property.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110802"},"PeriodicalIF":1.7,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128213","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}
引用次数: 0
Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-12-06 DOI: 10.1016/j.jfa.2024.110790
Cédric Arhancet
{"title":"Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras","authors":"Cédric Arhancet","doi":"10.1016/j.jfa.2024.110790","DOIUrl":"10.1016/j.jfa.2024.110790","url":null,"abstract":"<div><div>We investigate a new class of unital quantum channels on <span><math><msub><mrow><mi>M</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msup></mrow></msub></math></span>, acting as radial multipliers when we identify the matrix algebra <span><math><msub><mrow><mi>M</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msup></mrow></msub></math></span> with a finite-dimensional fermion algebra. Our primary contribution lies in the precise computation of the (optimal) rate at which classical information can be transmitted through these channels from a sender to a receiver when they share an unlimited amount of entanglement. Our approach relies on new connections between fermion algebras with the <em>n</em>-dimensional discrete hypercube <span><math><msup><mrow><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Significantly, our calculations yield exact values applicable to the operators of the fermionic Ornstein-Uhlenbeck semigroup. This advancement not only provides deeper insights into the structure and behaviour of these channels but also enhances our understanding of Quantum Information Theory in a dimension-independent context.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110790"},"PeriodicalIF":1.7,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143092983","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
Time-dependent flows and their applications in parabolic-parabolic Patlak-Keller-Segel systems Part I: Alternating flows
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-12-06 DOI: 10.1016/j.jfa.2024.110786
Siming He
{"title":"Time-dependent flows and their applications in parabolic-parabolic Patlak-Keller-Segel systems Part I: Alternating flows","authors":"Siming He","doi":"10.1016/j.jfa.2024.110786","DOIUrl":"10.1016/j.jfa.2024.110786","url":null,"abstract":"<div><div>We consider the three-dimensional parabolic-parabolic Patlak-Keller-Segel equations (PKS) subject to ambient flows. Without the ambient fluid flow, the equation is super-critical in three-dimension and has finite-time blow-up solutions with arbitrarily small <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-mass. In this study, we show that a family of time-dependent alternating shear flows, inspired by the clever ideas of Tarek Elgindi <span><span>[39]</span></span>, can suppress the chemotactic blow-up in these systems.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110786"},"PeriodicalIF":1.7,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128207","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
Highly singular (frequentially sparse) steady solutions for the 2D Navier–Stokes equations on the torus 环面上二维Navier-Stokes方程的高度奇异（频繁稀疏）稳态解
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-11-22 DOI: 10.1016/j.jfa.2024.110761
Pierre Gilles Lemarié-Rieusset
{"title":"Highly singular (frequentially sparse) steady solutions for the 2D Navier–Stokes equations on the torus","authors":"Pierre Gilles Lemarié-Rieusset","doi":"10.1016/j.jfa.2024.110761","DOIUrl":"10.1016/j.jfa.2024.110761","url":null,"abstract":"<div><div>We construct non-trivial steady solutions in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> for the 2D Navier–Stokes equations on the torus. In particular, the solutions are not square integrable, so that we have to introduce a notion of special (non square integrable) solutions.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 4","pages":"Article 110761"},"PeriodicalIF":1.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743690","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
Normalized ground states for Schrödinger equations on metric graphs with nonlinear point defects 具有非线性点缺陷的度量图上Schrödinger方程的归一化基态
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-11-22 DOI: 10.1016/j.jfa.2024.110760
Filippo Boni , Simone Dovetta , Enrico Serra
{"title":"Normalized ground states for Schrödinger equations on metric graphs with nonlinear point defects","authors":"Filippo Boni ,&nbsp;Simone Dovetta ,&nbsp;Enrico Serra","doi":"10.1016/j.jfa.2024.110760","DOIUrl":"10.1016/j.jfa.2024.110760","url":null,"abstract":"<div><div>We investigate the existence of normalized ground states for Schrödinger equations on noncompact metric graphs in presence of nonlinear point defects, described by nonlinear <em>δ</em>-interactions at some of the vertices of the graph. For graphs with finitely many vertices, we show that ground states exist for every mass and every <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-subcritical power. For graphs with infinitely many vertices, we focus on periodic graphs and, in particular, on <span><math><mi>Z</mi></math></span>-periodic graphs and on a prototypical <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-periodic graph, the two–dimensional square grid. We provide a set of results unravelling nontrivial threshold phenomena both on the mass and on the nonlinearity power, showing the strong dependence of the ground state problem on the interplay between the degree of periodicity of the graph, the total number of point defects and their dislocation in the graph.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 4","pages":"Article 110760"},"PeriodicalIF":1.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743622","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
Bounds for the kernel of the (κ,a)-generalized Fourier transform 广义傅里叶变换（κ,a）核函数的界
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-11-22 DOI: 10.1016/j.jfa.2024.110755
Hendrik De Bie , Pan Lian , Frederick Maes
{"title":"Bounds for the kernel of the (κ,a)-generalized Fourier transform","authors":"Hendrik De Bie ,&nbsp;Pan Lian ,&nbsp;Frederick Maes","doi":"10.1016/j.jfa.2024.110755","DOIUrl":"10.1016/j.jfa.2024.110755","url":null,"abstract":"<div><div>In this paper, we study the pointwise bounds for the kernel of the <span><math><mo>(</mo><mi>κ</mi><mo>,</mo><mi>a</mi><mo>)</mo></math></span>-generalized Fourier transform with <span><math><mi>κ</mi><mo>≡</mo><mn>0</mn></math></span>, introduced by Ben Saïd, Kobayashi and Ørsted. We present explicit formulas for the case <span><math><mi>a</mi><mo>=</mo><mn>4</mn></math></span>, which show that the kernels can exhibit polynomial growth. Subsequently, we provide a polynomial bound for the even dimensional kernel for this transform, focusing on the cases with finite order. Furthermore, by utilizing an estimation for the Prabhakar function, it is found that the <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mi>a</mi><mo>)</mo></math></span>-generalized Fourier kernel is bounded by a constant when <span><math><mi>a</mi><mo>&gt;</mo><mn>1</mn></math></span> and <span><math><mi>m</mi><mo>≥</mo><mn>2</mn></math></span>, except within an angular domain that diminishes as <span><math><mi>a</mi><mo>→</mo><mo>∞</mo></math></span>. As a byproduct, we prove that the <span><math><mo>(</mo><mn>0</mn><mo>,</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>ℓ</mi></mrow></msup><mo>/</mo><mi>n</mi><mo>)</mo></math></span>-generalized Fourier kernel is uniformly bounded, when <span><math><mi>m</mi><mo>=</mo><mn>2</mn></math></span> and <span><math><mi>ℓ</mi><mo>,</mo><mi>n</mi><mo>∈</mo><mi>N</mi></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 4","pages":"Article 110755"},"PeriodicalIF":1.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743689","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
Local invariants of conformally deformed non-commutative tori II: Multiple operator integrals
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-11-22 DOI: 10.1016/j.jfa.2024.110754
Teun van Nuland , Fedor Sukochev , Dmitriy Zanin
{"title":"Local invariants of conformally deformed non-commutative tori II: Multiple operator integrals","authors":"Teun van Nuland ,&nbsp;Fedor Sukochev ,&nbsp;Dmitriy Zanin","doi":"10.1016/j.jfa.2024.110754","DOIUrl":"10.1016/j.jfa.2024.110754","url":null,"abstract":"<div><div>We explicitly compute the local invariants (heat kernel coefficients) of a conformally deformed non-commutative <em>d</em>-torus using multiple operator integrals. We derive a recursive formula that easily produces an explicit expression for the local invariants of any order <em>k</em> and in any dimension <em>d</em>. Our recursive formula can conveniently produce all formulas related to the modular operator, which before were obtained in incremental steps for <span><math><mi>d</mi><mo>∈</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo></math></span> and <span><math><mi>k</mi><mo>∈</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>}</mo></math></span>. We exemplify this by writing down some known (<span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>, <span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span>) and some novel (<span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>, <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span>) formulas in the modular operator.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 4","pages":"Article 110754"},"PeriodicalIF":1.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178223","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}
引用次数: 0
Alberti's rank one theorem and quasiconformal mappings in metric measure spaces 测度空间中的Alberti秩一定理与拟共形映射
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-11-22 DOI: 10.1016/j.jfa.2024.110758
Panu Lahti
{"title":"Alberti's rank one theorem and quasiconformal mappings in metric measure spaces","authors":"Panu Lahti","doi":"10.1016/j.jfa.2024.110758","DOIUrl":"10.1016/j.jfa.2024.110758","url":null,"abstract":"<div><div>We investigate a version of Alberti's rank one theorem in Ahlfors regular metric spaces, as well as a connection with quasiconformal mappings. More precisely, we give a proof of the rank one theorem that partially follows along the usual steps, but the most crucial step consists in showing for <span><math><mi>f</mi><mo>∈</mo><mrow><mi>BV</mi></mrow><mo>(</mo><mi>X</mi><mo>;</mo><mi>Y</mi><mo>)</mo></math></span> that at <span><math><msup><mrow><mo>‖</mo><mi>D</mi><mi>f</mi><mo>‖</mo></mrow><mrow><mi>s</mi></mrow></msup></math></span>-a.e. <span><math><mi>x</mi><mo>∈</mo><mi>X</mi></math></span>, the mapping <em>f</em> “behaves non-quasiconformally”.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 4","pages":"Article 110758"},"PeriodicalIF":1.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743623","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 Whitney extension problem for manifolds
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-11-20 DOI: 10.1016/j.jfa.2024.110753
Kevin O'Neill
{"title":"A Whitney extension problem for manifolds","authors":"Kevin O'Neill","doi":"10.1016/j.jfa.2024.110753","DOIUrl":"10.1016/j.jfa.2024.110753","url":null,"abstract":"<div><div>The purpose of this paper is to address a manifold-based version of Whitney's extension problem: Given a compact set <span><math><mi>E</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, how can we tell if there exists a <em>d</em>-dimensional, <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>-smooth manifold <span><math><mi>M</mi><mo>⊃</mo><mi>E</mi></math></span>? We provide an answer for compact manifolds with boundary in terms of a Glaeser refinement much like that used in the solution of the classical Whitney extension problem and a topological condition. This condition is the existence of a continuous selection for Grassmannian-valued functions, meant to reflect the collection of possible tangent spaces. We demonstrate the necessity of this condition in general and its non-redundancy in an example, while also showing it need not be checked when <span><math><mi>d</mi><mo>=</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110753"},"PeriodicalIF":1.7,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143093263","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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