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On the global in time existence and uniqueness of solutions to the Boltzmann hierarchy 玻尔兹曼级数解的全局时间存在唯一性
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111079
Ioakeim Ampatzoglou , Joseph K. Miller , Nataša Pavlović , Maja Tasković
{"title":"On the global in time existence and uniqueness of solutions to the Boltzmann hierarchy","authors":"Ioakeim Ampatzoglou ,&nbsp;Joseph K. Miller ,&nbsp;Nataša Pavlović ,&nbsp;Maja Tasković","doi":"10.1016/j.jfa.2025.111079","DOIUrl":"10.1016/j.jfa.2025.111079","url":null,"abstract":"<div><div>In this paper we establish the global in time existence and uniqueness of solutions to the Boltzmann hierarchy, a hierarchy of equations instrumental for the rigorous derivation of the Boltzmann equation from many particles. Inspired by available <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-based a-priori estimate for solutions to the Boltzmann equation, we develop the polynomially weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> a-priori bounds for solutions to the Boltzmann hierarchy and handle the factorial growth of the number of terms in the Dyson's series by reorganizing the sum through a combinatorial technique known as the Klainerman-Machedon board game argument. This paper is the first work that exploits such a combinatorial technique in conjunction with an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-based estimate to prove uniqueness of the mild solutions to the Boltzmann hierarchy. Our proof of existence of global in time mild solutions to the Boltzmann hierarchy for admissible initial data is constructive and it employs known global in time solutions to the Boltzmann equation via a Hewitt-Savage type theorem.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111079"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242641","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
Regularity for the fractional p-Laplace equation 分数阶p-拉普拉斯方程的正则性
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111078
Verena Bögelein , Frank Duzaar , Naian Liao , Giovanni Molica Bisci , Raffaella Servadei
{"title":"Regularity for the fractional p-Laplace equation","authors":"Verena Bögelein ,&nbsp;Frank Duzaar ,&nbsp;Naian Liao ,&nbsp;Giovanni Molica Bisci ,&nbsp;Raffaella Servadei","doi":"10.1016/j.jfa.2025.111078","DOIUrl":"10.1016/j.jfa.2025.111078","url":null,"abstract":"<div><div>Higher Sobolev and Hölder regularity is studied for local weak solutions of the fractional <em>p</em>-Laplace equation of order <em>s</em> in the case <span><math><mi>p</mi><mo>≥</mo><mn>2</mn></math></span>. Depending on the regime considered, i.e.<span><span><span><math><mn>0</mn><mo>&lt;</mo><mi>s</mi><mo>≤</mo><mfrac><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow><mrow><mi>p</mi></mrow></mfrac><mspace></mspace><mtext>or</mtext><mspace></mspace><mfrac><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow><mrow><mi>p</mi></mrow></mfrac><mo>&lt;</mo><mi>s</mi><mo>&lt;</mo><mn>1</mn><mo>,</mo></math></span></span></span> precise local estimates are proven. The relevant estimates are stable if the fractional order <em>s</em> reaches 1; the known Sobolev regularity estimates for the local <em>p</em>-Laplace are recovered. The case <span><math><mi>p</mi><mo>=</mo><mn>2</mn></math></span> reproduces the almost <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mi>loc</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>s</mi><mo>,</mo><mn>2</mn></mrow></msubsup></math></span>-regularity for the fractional Laplace equation of any order <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111078"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144262935","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
The weak convergence for a measure related to a class of conformally invariant fully nonlinear operator 一类共形不变全非线性算子测度的弱收敛性
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111080
Xi-Nan Ma , Wangzhe Wu
{"title":"The weak convergence for a measure related to a class of conformally invariant fully nonlinear operator","authors":"Xi-Nan Ma ,&nbsp;Wangzhe Wu","doi":"10.1016/j.jfa.2025.111080","DOIUrl":"10.1016/j.jfa.2025.111080","url":null,"abstract":"<div><div>Trudinger-Wang introduced the notion of k-Hessian measure associated with k-convex functions, not necessarily continuous, and proved the weak continuity of the associated k-Hessian measure with respect to local <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> convergence in 1999. In this paper we find a special divergence structure for the <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>-Yamabe operator which is conformally invariant, and prove the weak continuity of the <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>-Yamabe operator with respect to local <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> convergence.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111080"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203215","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 improved multiplier theorem on rank one noncompact symmetric spaces 秩1非紧对称空间上的一个改进乘子定理
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111082
Błażej Wróbel
{"title":"An improved multiplier theorem on rank one noncompact symmetric spaces","authors":"Błażej Wróbel","doi":"10.1016/j.jfa.2025.111082","DOIUrl":"10.1016/j.jfa.2025.111082","url":null,"abstract":"<div><div>We prove a multiplier theorem on rank one noncompact symmetric spaces which improves aspects of existing results. Namely, we partially drop specific assumptions on the multiplier function such as a Mikhlin-Hörmander condition. This is replaced by a requirement that parts of the multiplier function on the critical <em>p</em> strip give rise to bounded Fourier multipliers.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111082"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221356","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
Ancient and expanding spin ALE Ricci flows 古老而膨胀的自旋ALE Ricci流
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-27 DOI: 10.1016/j.jfa.2025.111062
Isaac M. Lopez, Tristan Ozuch
{"title":"Ancient and expanding spin ALE Ricci flows","authors":"Isaac M. Lopez,&nbsp;Tristan Ozuch","doi":"10.1016/j.jfa.2025.111062","DOIUrl":"10.1016/j.jfa.2025.111062","url":null,"abstract":"<div><div>We classify spin ALE ancient Ricci flows and spin ALE expanding solitons with suitable groups at infinity. In particular, the only spin ancient Ricci flows with groups at infinity in <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span> and mild decay at infinity are hyperkähler ALE metrics. The main idea of the proof, of independent interest, consists in showing that the large-scale behavior of Perelman's <em>μ</em>-functional on any ALE orbifold with non-negative scalar curvature is controlled by a renormalized <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>ALE</mi></mrow></msub></math></span>-functional related to a notion of weighted mass.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111062"},"PeriodicalIF":1.7,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242639","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
Strict comparison and stable rank one 严格比较，稳定排名第一
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-23 DOI: 10.1016/j.jfa.2025.111065
Huaxin Lin
{"title":"Strict comparison and stable rank one","authors":"Huaxin Lin","doi":"10.1016/j.jfa.2025.111065","DOIUrl":"10.1016/j.jfa.2025.111065","url":null,"abstract":"<div><div>Let <em>A</em> be a <em>σ</em>-unital finite simple <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra which has strict comparison property. We show that if the rank map Γ from the Cuntz semigroup to certain lower semicontinuous affine functions is surjective, then <em>A</em> has tracial approximate oscillation zero and stable rank one. Equivalently, if <em>A</em> is a <em>σ</em>-unital finite simple <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra which has an almost unperforated and almost divisible Cuntz semigroup, then <em>A</em> has stable rank one and tracial approximate oscillation zero.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111065"},"PeriodicalIF":1.7,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144196103","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 steady states for the Vlasov-Schrödinger-Poisson system 关于Vlasov-Schrödinger-Poisson系统的稳态
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-23 DOI: 10.1016/j.jfa.2025.111069
Younghun Hong , Sangdon Jin
{"title":"On steady states for the Vlasov-Schrödinger-Poisson system","authors":"Younghun Hong ,&nbsp;Sangdon Jin","doi":"10.1016/j.jfa.2025.111069","DOIUrl":"10.1016/j.jfa.2025.111069","url":null,"abstract":"<div><div>The Vlasov-Schrödinger-Poisson system is a kinetic-quantum hybrid model describing quasi-lower dimensional electron gases. For this system, we construct a large class of 2D kinetic/1D quantum steady states in a bounded domain as generalized free energy minimizers, and we show their finite subband structure, monotonicity, uniqueness and <em>conditional</em> dynamical stability. Our proof is based on the concentration-compactness principle, but some additional difficulties arise due to lack of compactness originated from the hybrid nature (see <span><span>Remark 1.9</span></span>). To overcome the difficulties, we introduce a 3-step refinement of a minimizing sequence by rearrangement and partial minimization problems, and the coercivity lemma for the free energy (<span><span>Lemma 5.3</span></span>) is crucially employed.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111069"},"PeriodicalIF":1.7,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138046","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
Large-scale dispersive estimates for acoustic operators: Homogenization meets localization 声学算子的大规模色散估计：均质化满足局域化
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-23 DOI: 10.1016/j.jfa.2025.111068
Mitia Duerinckx , Antoine Gloria
{"title":"Large-scale dispersive estimates for acoustic operators: Homogenization meets localization","authors":"Mitia Duerinckx ,&nbsp;Antoine Gloria","doi":"10.1016/j.jfa.2025.111068","DOIUrl":"10.1016/j.jfa.2025.111068","url":null,"abstract":"<div><div>This work relates quantitatively homogenization to Anderson localization for acoustic operators in disordered media. By blending dispersive estimates for homogenized operators and quantitative homogenization of the wave equation, we derive large-scale dispersive estimates for waves in disordered media that we apply to the spreading of low-energy eigenstates. This gives a short and direct proof that the lower spectrum of the acoustic operator is purely absolutely continuous in case of periodic media, and it further provides new lower bounds on the localization length of possible eigenstates in case of quasiperiodic or random media.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111068"},"PeriodicalIF":1.7,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169797","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
The Monge-Ampère system in dimension two: A regularity improvement 二维的monge - ampantere系统：一种正则性改进
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-23 DOI: 10.1016/j.jfa.2025.111064
Marta Lewicka
{"title":"The Monge-Ampère system in dimension two: A regularity improvement","authors":"Marta Lewicka","doi":"10.1016/j.jfa.2025.111064","DOIUrl":"10.1016/j.jfa.2025.111064","url":null,"abstract":"<div><div>We prove a convex integration result for the Monge-Ampère system introduced in <span><span>[7]</span></span>, in case of dimension <span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span> and arbitrary codimension <span><math><mi>k</mi><mo>≥</mo><mn>1</mn></math></span>. Our prior result <span><span>[8]</span></span> stated flexibility up to the Hölder regularity <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mo>+</mo><mn>4</mn><mo>/</mo><mi>k</mi></mrow></mfrac></mrow></msup></math></span>, whereas presently we achieve flexibility up to <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span> when <span><math><mi>k</mi><mo>≥</mo><mn>4</mn></math></span> and up to <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mfrac><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msup><mo>−</mo><mn>1</mn></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></msup></math></span> for any <em>k</em>. This first result uses the approach closest to that of Källen <span><span>[6]</span></span> in the context of the isometric immersion problem, while the second result uses the double iteration procedure from <span><span>[7]</span></span> combined with the approach of Cao-Hirsch-Inauen <span><span>[1]</span></span>, agreeing with it for <span><math><mi>k</mi><mo>=</mo><mn>1</mn></math></span> at the Hölder regularity up to <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111064"},"PeriodicalIF":1.7,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169794","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
Weighted inertia-dissipation-energy approach to doubly nonlinear wave equations 双非线性波动方程的加权惯性-耗散-能量方法
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-22 DOI: 10.1016/j.jfa.2025.111067
Goro Akagi , Verena Bögelein , Alice Marveggio , Ulisse Stefanelli
{"title":"Weighted inertia-dissipation-energy approach to doubly nonlinear wave equations","authors":"Goro Akagi ,&nbsp;Verena Bögelein ,&nbsp;Alice Marveggio ,&nbsp;Ulisse Stefanelli","doi":"10.1016/j.jfa.2025.111067","DOIUrl":"10.1016/j.jfa.2025.111067","url":null,"abstract":"<div><div>We discuss a variational approach to doubly nonlinear wave equations of the form <span><math><mi>ρ</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>+</mo><mi>g</mi><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span>. This approach hinges on the minimization of a parameter-dependent family of uniformly convex functionals over entire trajectories, namely the so-called Weighted Inertia-Dissipation-Energy (WIDE) functionals. We prove that the WIDE functionals admit minimizers and that the corresponding Euler-Lagrange system is solvable in the strong sense. Moreover, we check that the parameter-dependent minimizers converge, up to subsequences, to a solution of the target doubly nonlinear wave equation as the parameter goes to 0. The analysis relies on specific estimates on the WIDE minimizers, on the decomposition of the subdifferential of the WIDE functional, and on the identification of the nonlinearities in the limit. Eventually, we investigate the viscous limit <span><math><mi>ρ</mi><mo>→</mo><mn>0</mn></math></span>, both at the functional level and on that of the equation.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111067"},"PeriodicalIF":1.7,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169795","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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