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A remark on the weak Harnack inequality
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-05 DOI: 10.1016/j.jmaa.2025.129446
Diego Maldonado
{"title":"A remark on the weak Harnack inequality","authors":"Diego Maldonado","doi":"10.1016/j.jmaa.2025.129446","DOIUrl":"10.1016/j.jmaa.2025.129446","url":null,"abstract":"<div><div>A short proof of the weak Harnack inequality based on the critical-density and double-ball properties is presented. The proof relies on basic properties of Muckenhoupt weights in general spaces of homogenous type.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129446"},"PeriodicalIF":1.2,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 existence and uniqueness of classical solutions for a compressible Oldroyd-B model with vacuum
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-05 DOI: 10.1016/j.jmaa.2025.129450
Yubi Yin, Xingyang Zhang
{"title":"Local existence and uniqueness of classical solutions for a compressible Oldroyd-B model with vacuum","authors":"Yubi Yin,&nbsp;Xingyang Zhang","doi":"10.1016/j.jmaa.2025.129450","DOIUrl":"10.1016/j.jmaa.2025.129450","url":null,"abstract":"<div><div>In this paper, we consider compressible Oldroyd-B equations in a bounded or unbounded domain Ω of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. Assuming that the initial data satisfy a natural compatibility condition, we show the local existence and uniqueness of the classical solutions for Oldroyd-B equations through some high-order estimations with respect to time weighting. To obtain the result, the initial density does not need to differ from zero and may vanish in an open subset (vacuum) of Ω or decay at infinity when Ω is unbounded.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129450"},"PeriodicalIF":1.2,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Asymptotics for k-crank of k-colored partitions
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-05 DOI: 10.1016/j.jmaa.2025.129447
Helen W.J. Zhang , Ying Zhong
{"title":"Asymptotics for k-crank of k-colored partitions","authors":"Helen W.J. Zhang ,&nbsp;Ying Zhong","doi":"10.1016/j.jmaa.2025.129447","DOIUrl":"10.1016/j.jmaa.2025.129447","url":null,"abstract":"<div><div>In this paper, we obtain asymptotic formulas for the <em>k</em>-crank of <em>k</em>-colored partitions. Let <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>a</mi><mo>,</mo><mi>c</mi><mo>;</mo><mi>n</mi><mo>)</mo></math></span> denote the number of <em>k</em>-colored partitions of <em>n</em> with a <em>k</em>-crank congruent to <em>a</em> mod <em>c</em>. For the cases <span><math><mi>k</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></math></span>, Fu and Tang derived several inequality relations for <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>a</mi><mo>,</mo><mi>c</mi><mo>;</mo><mi>n</mi><mo>)</mo></math></span> using generating functions. We employ the Hardy-Ramanujan Circle Method to extend the results of Fu and Tang. Furthermore, strict log-subadditivity for <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>a</mi><mo>,</mo><mi>c</mi><mo>;</mo><mi>n</mi><mo>)</mo></math></span> is established.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129447"},"PeriodicalIF":1.2,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Approximation of feedback gains for the Oseen system
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-04 DOI: 10.1016/j.jmaa.2025.129418
Mehdi Badra, Jean-Pierre Raymond
{"title":"Approximation of feedback gains for the Oseen system","authors":"Mehdi Badra,&nbsp;Jean-Pierre Raymond","doi":"10.1016/j.jmaa.2025.129418","DOIUrl":"10.1016/j.jmaa.2025.129418","url":null,"abstract":"<div><div>We consider the Oseen system with a Dirichlet boundary control, and its semidiscrete approximation by a finite element method (FEM). We show that these two systems fit with the abstract setting recently introduced in <span><span>[5]</span></span>. We obtain convergence rates for Riccati based feedback laws and their discrete approximation, in terms of the discretization parameter <em>h</em> (the mesh size of the FEM). We also prove convergence rates between the solution of the closed-loop Oseen system and the solution of the semidiscrete closed-loop Oseen system. These results are based on new error estimates, previously known for the Stokes system in polyhedral or polygonal convex domains, that we have recently extended to the Oseen system in polyhedral (or polygonal) convex or non-convex domains. We also prove a uniform bound for the discrete control operator <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span>, which seems to be totally new in the context of the numerical approximation of feedback laws.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129418"},"PeriodicalIF":1.2,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Boundedness and compactness for differences of composition operators between Bergman spaces on strongly pseudoconvex domains
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-04 DOI: 10.1016/j.jmaa.2025.129440
Ly Kim Ha
{"title":"Boundedness and compactness for differences of composition operators between Bergman spaces on strongly pseudoconvex domains","authors":"Ly Kim Ha","doi":"10.1016/j.jmaa.2025.129440","DOIUrl":"10.1016/j.jmaa.2025.129440","url":null,"abstract":"<div><div>This article deals with boundedness and compactness of differences of composition operators <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>−</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>v</mi></mrow></msub></math></span> between holomorphic Bergman spaces on strongly Levi-pseudoconvex domains in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129440"},"PeriodicalIF":1.2,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 monotony of the q−Bessel functions
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-04 DOI: 10.1016/j.jmaa.2025.129439
Yücel Özkan , Semra Korkmaz , Erhan Deniz
{"title":"The monotony of the q−Bessel functions","authors":"Yücel Özkan ,&nbsp;Semra Korkmaz ,&nbsp;Erhan Deniz","doi":"10.1016/j.jmaa.2025.129439","DOIUrl":"10.1016/j.jmaa.2025.129439","url":null,"abstract":"<div><div>In this paper, we prove a monotonicity property for the normalized Jackson and Hahn-Exton <em>q</em>-Bessel functions using the method of subordination factor sequences. Additionally, in the special case of <span><math><mi>q</mi><mo>→</mo><mn>1</mn></math></span>, we obtain the result of Cotîrlá and Szász (2024) <span><span>[8]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129439"},"PeriodicalIF":1.2,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
About solutions for gradient-type cooperative systems beyond extremal parameter
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-03 DOI: 10.1016/j.jmaa.2025.129436
Steffânio Moreno
{"title":"About solutions for gradient-type cooperative systems beyond extremal parameter","authors":"Steffânio Moreno","doi":"10.1016/j.jmaa.2025.129436","DOIUrl":"10.1016/j.jmaa.2025.129436","url":null,"abstract":"<div><div>We investigate the existence and non-existence of solutions for cooperative elliptic gradient-type systems, depending on the real parameters <em>λ</em> and <em>μ</em>. Our approach, based on a refined analysis of the Nehari manifold associated with the problem, allows us to establish the existence and multiplicity of solutions by minimizing the associated energy functional over components of the Nehari set for parameters beyond the extremal parameter <span><math><msup><mrow><mi>λ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129436"},"PeriodicalIF":1.2,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Analysis of a free boundary problem on stratified Lie group
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-03 DOI: 10.1016/j.jmaa.2025.129438
Sabri Bensid
{"title":"Analysis of a free boundary problem on stratified Lie group","authors":"Sabri Bensid","doi":"10.1016/j.jmaa.2025.129438","DOIUrl":"10.1016/j.jmaa.2025.129438","url":null,"abstract":"<div><div>We present a variational framework for studying the existence of solutions of a class of elliptic free boundary problems on stratified Lie groups. Using the important monotonicity result in a Non-Euclidean setup, we prove that our solution is the limit of mountain pass points of a sequence of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-functionals approximating the energy.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129438"},"PeriodicalIF":1.2,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 properties of the solutions to the (p,q)-harmonic functions
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-03 DOI: 10.1016/j.jmaa.2025.129437
Peijin Li , Qinghong Luo , Saminathan Ponnusamy
{"title":"On properties of the solutions to the (p,q)-harmonic functions","authors":"Peijin Li ,&nbsp;Qinghong Luo ,&nbsp;Saminathan Ponnusamy","doi":"10.1016/j.jmaa.2025.129437","DOIUrl":"10.1016/j.jmaa.2025.129437","url":null,"abstract":"<div><div>Suppose <span><math><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mi>R</mi><mo>﹨</mo><msup><mrow><mi>Z</mi></mrow><mrow><mo>−</mo></mrow></msup></math></span> such that <span><math><mi>p</mi><mo>+</mo><mi>q</mi><mo>&gt;</mo><mo>−</mo><mn>1</mn></math></span>. The aim of this paper is to establish properties of the <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-harmonic functions in the unit disc <span><math><mo>|</mo><mi>z</mi><mo>|</mo><mo>&lt;</mo><mn>1</mn></math></span> in the complex plane <span><math><mi>C</mi></math></span>. We obtain the boundedness and the Lipschitz continuity with respect to the hyperbolic metric for <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-harmonic functions. In particular, for <span><math><mi>p</mi><mo>=</mo><mi>q</mi><mo>&gt;</mo><mo>−</mo><mn>1</mn></math></span>, we get the Heinz type inequality on the unit circle <span><math><mo>|</mo><mi>z</mi><mo>|</mo><mo>=</mo><mn>1</mn></math></span>. As an application, a Landau type theorem of <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-harmonic functions is established.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129437"},"PeriodicalIF":1.2,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Admissibility and generalized nonuniform dichotomies for nonautonomous random dynamical systems
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-03 DOI: 10.1016/j.jmaa.2025.129441
Davor Dragičević , César M. Silva , Helder Vilarinho
{"title":"Admissibility and generalized nonuniform dichotomies for nonautonomous random dynamical systems","authors":"Davor Dragičević ,&nbsp;César M. Silva ,&nbsp;Helder Vilarinho","doi":"10.1016/j.jmaa.2025.129441","DOIUrl":"10.1016/j.jmaa.2025.129441","url":null,"abstract":"<div><div>In this paper, we introduce generalized dichotomies for nonautonomous random linear dynamical systems acting on arbitrary Banach spaces, and obtain their complete characterization in terms of an appropriate admissibility property. These generalized dichotomies are associated to growth rates satisfying mild conditions and they include the standard exponential behavior as a very particular case. As a nontrivial application, we establish the robustness property of such dichotomies under small (linear) perturbations.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129441"},"PeriodicalIF":1.2,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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