Journal of Mathematical Analysis and Applications最新文献

{"title":"A priori estimates for Monge-Ampère equation with a gradient term","authors":"Pang Xu,&nbsp;Xin-An Ren","doi":"10.1016/j.jmaa.2025.129765","DOIUrl":"10.1016/j.jmaa.2025.129765","url":null,"abstract":"<div><div>This paper is concerned with the Monge-Ampère equation with a gradient term on Kähler manifolds. It is proved that the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> estimate and <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> estimate depend only on the lower bound of the solutions. Moreover, the constant in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> estimate is relaxed to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup></math></span> norm.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129765"},"PeriodicalIF":1.2,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254049","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}

{"title":"Existence and exponential decay of bound state solutions for the Brown-Ravenhall operator with a critical potential for non-confining systems in genuinely two-dimensional spaces","authors":"Magno B. Alves ,&nbsp;Daniel H.T. Franco ,&nbsp;Emmanuel Pereira","doi":"10.1016/j.jmaa.2025.129754","DOIUrl":"10.1016/j.jmaa.2025.129754","url":null,"abstract":"<div><div>We study the Brown-Ravenhall operator (the suitably projected Dirac operator) in dimension 2 using the Foldy-Wouthuysen unitary transformation. This allows us to write the operator in diagonalized form, so that the kinetic energy is equal to <span><math><mo>〈</mo><mi>ψ</mi><mo>,</mo><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>+</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mi>ψ</mi><mo>〉</mo></math></span>. This suggests that we use some interesting results found in recent literature for equations driven by the fractional operator <span><math><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>+</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mi>s</mi></mrow></msup></math></span> with <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> and <span><math><mi>m</mi><mo>&gt;</mo><mn>0</mn></math></span>. Here, we are interested in the Brown-Ravenhall operator perturbed by a short-range attractive potential given by a Bessel-Macdonald function (also known as <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-potential) to model relativistic effects in graphene. The existence of bound states for the Brown-Ravenhall operator with the <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-potential is proven using a variant of the Caffarelli-Silvestre extension method, which permits to characterize <span><math><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>+</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span> as an operator that maps a Dirichlet boundary condition to a Neumann-type condition via an extension problem in the upper-half space <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>3</mn></mrow></msubsup></math></span>. In this process, the minimization occurs for an auxiliary energy functional associated with the weak solutions of the Neumann problem, defined on <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>3</mn></mrow></msubsup><mo>;</mo><mi>C</mi><mo>)</mo></math></span>. In addition, the lower bound for the smallest eigenvalue is established via Herbst operator. Exponential decay, in an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> sense, of the bound states of the Brown-Ravenhall operator with the <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-potential is also investigated.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129754"},"PeriodicalIF":1.2,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241386","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}

{"title":"Existence and nonuniqueness of solutions for flow driven by a revolving hybrid nanofluid above a stationary disk","authors":"Dibjyoti Mondal,&nbsp;Abhijit Das,&nbsp;Amit Kumar Pandey","doi":"10.1016/j.jmaa.2025.129743","DOIUrl":"10.1016/j.jmaa.2025.129743","url":null,"abstract":"<div><div>The qualitative and quantitative properties of solutions associated with the nonlinear and coupled boundary value problems (BVPs) that describe the thermo-hydrodynamics of a hybrid nanofluid rotating over a stationary disk with suction are under investigation. First, essential a priori boundedness conditions are derived, and proof guaranteeing the existence of a solution to these BVPs is given. Next, numerically, it is shown that solutions to these equations are non-unique, exhibiting two solution branches to the problem within a particular range of the suction parameter. The influence of relevant flow parameters on radial and tangential shear stresses, Nusselt number, dimensionless velocity, and temperature profiles is presented graphically for both branches of the solution, with a detailed discussion of their physical significance. The results show that the oscillatory behavior of the first solution decreases with increased suction, whereas, in contrast, the second solution branch continues to oscillate as suction increases and extends indefinitely. Furthermore, a linear temporal stability analysis shows that only the first solution branch is stable, while the second branch is unstable. Finally, an asymptotic expression providing insights into the large suction behavior is also derived.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129743"},"PeriodicalIF":1.2,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254047","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}

{"title":"Analysis of a nonisothermal and conserved phase field system with inertial term","authors":"Pierluigi Colli ,&nbsp;Shunsuke Kurima","doi":"10.1016/j.jmaa.2025.129744","DOIUrl":"10.1016/j.jmaa.2025.129744","url":null,"abstract":"<div><div>This paper deals with a conserved phase field system that couples the energy balance equation with a Cahn–Hilliard type system including temperature and the inertial term for the order parameter. In the case without inertial term, the system under study was introduced by Caginalp. The inertial term is motivated by the occurrence of rapid phase transformation processes in nonequilibrium dynamics. A double-well potential is well chosen and the related nonlinearity governing the evolution is assumed to satisfy a suitable growth condition. The viscous variant of the Cahn–Hilliard system is also considered along with the inertial term. The existence of a global solution is proved via the analysis of some approximate problems with Yosida regularizations, and the use of the Cauchy–Lipschitz–Picard theorem in an abstract setting. Moreover, we study the convergence of the system, with or without the viscous term, as the inertial coefficient tends to zero.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129744"},"PeriodicalIF":1.2,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222777","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}

{"title":"Boundedness of solutions to an alarm-taxis model with/without growth sources","authors":"Dongze Yan,&nbsp;Changchun Liu","doi":"10.1016/j.jmaa.2025.129747","DOIUrl":"10.1016/j.jmaa.2025.129747","url":null,"abstract":"<div><div>This paper is a further step in the study of the global boundedness of solutions for a predator-prey model with alarm-taxis. For cases where there are no logistic source terms, it will be shown that if certain parameters in the reaction functions satisfy specific conditions, then the classical solution exists globally and is bounded in higher dimensions. For the case that both the predators have growth restrictions, when <span><math><mi>n</mi><mo>=</mo><mn>2</mn></math></span>, we find the relationship between the logistic degradation rates and the parameters in the functional response, which ensures the global existence and boundedness of the classical solution. Moreover, the results of this paper can encompass the boundedness results from <span><span>[14]</span></span> and <span><span>[21]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129747"},"PeriodicalIF":1.2,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222404","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}

{"title":"Lloc1-convergence of Jacobians of Sobolev homeomorphisms via area formula","authors":"Zofia Grochulska","doi":"10.1016/j.jmaa.2025.129741","DOIUrl":"10.1016/j.jmaa.2025.129741","url":null,"abstract":"<div><div>We prove that given a sequence of homeomorphisms <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>:</mo><mi>Ω</mi><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> convergent in <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msup><mo>(</mo><mi>Ω</mi><mo>,</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>, <span><math><mi>p</mi><mo>≥</mo><mn>1</mn></math></span> for <span><math><mi>n</mi><mo>=</mo><mn>2</mn></math></span> and <span><math><mi>p</mi><mo>&gt;</mo><mi>n</mi><mo>−</mo><mn>1</mn></math></span> for <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, to a homeomorphism <em>f</em> which maps sets of measure zero onto sets of measure zero, Jacobians <span><math><mi>J</mi><msub><mrow><mi>f</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> converge to <em>Jf</em> in <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>l</mi><mi>o</mi><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span>. We prove it via Federer's area formula and investigation of when <span><math><mo>|</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>E</mi><mo>)</mo><mo>|</mo><mo>→</mo><mo>|</mo><mi>f</mi><mo>(</mo><mi>E</mi><mo>)</mo><mo>|</mo></math></span> as <span><math><mi>k</mi><mo>→</mo><mo>∞</mo></math></span> for Borel subsets <span><math><mi>E</mi><mo>⋐</mo><mi>Ω</mi></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129741"},"PeriodicalIF":1.2,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144230169","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}

{"title":"On the stability of the viscoelastic Bénard problem in some classes of large data","authors":"Qunfeng Zhang,&nbsp;Hao Liu,&nbsp;Xianzhu Xiong","doi":"10.1016/j.jmaa.2025.129732","DOIUrl":"10.1016/j.jmaa.2025.129732","url":null,"abstract":"<div><div>In this paper, we investigate the Bénard problem of the incompressible viscoelastic fluids heated from below in a three-dimensional periodic cell, and establish the global (-in-time) existence result of unique strong solutions whenever the elasticity coefficient is sufficiently large relative to both norms (of energy space of solutions) of the initial velocity and the initial perturbation temperature. Our new result mathematically verifies that the elasticity under the large elasticity coefficient can inhibit the thermal instability even if both the initial velocity and the initial perturbation temperature are large. Moreover, the solutions also enjoy the exponential decay-in-time. In addition, using the method of vorticity estimates, we further derive that the convergence rate of the nonlinear system towards a linearized pressureless problem, as either time or elasticity coefficient approaches infinity, is in the form of <span><math><mi>c</mi><msup><mrow><mi>κ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>. Our converge rate is faster compared to the known rate <span><math><mi>c</mi><msup><mrow><mi>κ</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></math></span> first found by Jiang–Jiang in <span><span>[23]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129732"},"PeriodicalIF":1.2,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205132","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}

{"title":"Lp-Hodge decomposition with Sobolev classes in sub-Riemannian contact manifolds","authors":"Annalisa Baldi ,&nbsp;Alessandro Rosa","doi":"10.1016/j.jmaa.2025.129739","DOIUrl":"10.1016/j.jmaa.2025.129739","url":null,"abstract":"<div><div>Let <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span>. In this article we establish an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-Hodge decomposition theorem on sub-Riemannian compact contact manifolds without boundary, related to the Rumin complex of differential forms. Given an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>- Rumin's form, we adopt an approach in the spirit of Morrey's book <span><span>[26]</span></span> (further performed in <span><span>[18]</span></span>) to obtain a decomposition with higher regular “primitives” i.e. that belong to suitable Sobolev classes. Our proof relies on recent results obtained in <span><span>[4]</span></span> and <span><span>[6]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129739"},"PeriodicalIF":1.2,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144189460","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}

{"title":"On some logarithmic submajorisation inequalities of operators in finite von Neumann algebras","authors":"Ruifeng Sun,&nbsp;Jing Yang,&nbsp;Xingpeng Zhao","doi":"10.1016/j.jmaa.2025.129735","DOIUrl":"10.1016/j.jmaa.2025.129735","url":null,"abstract":"<div><div>In this paper, we prove some logarithmic submajorisation inequalities of operators in finite von Neumann algebras. In particular, the logarithmic submajorisation inequalities due to Boutata-Hirzallah-Kittaneh <span><span>[4]</span></span> are extended to the case of operators in a finite von Neumann algebra.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129735"},"PeriodicalIF":1.2,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144213198","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}

{"title":"An evolutionary vector-valued variational inequality and Lagrange multiplier","authors":"Davide Azevedo,&nbsp;Lisa Santos","doi":"10.1016/j.jmaa.2025.129746","DOIUrl":"10.1016/j.jmaa.2025.129746","url":null,"abstract":"<div><div>We prove existence and uniqueness of solution of an evolutionary vector-valued variational inequality defined in the convex set of vector valued functions <strong><em>v</em></strong> subject to the constraint <span><math><mo>|</mo><mi>v</mi><mo>|</mo><mo>≤</mo><mn>1</mn></math></span>. We show that we can write the variational inequality as a system of equations on the unknowns <span><math><mo>(</mo><mi>λ</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></span>, where <em>λ</em> is a (unique) Lagrange multiplier belonging to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> and <strong><em>u</em></strong> solves the variational inequality. Given data <span><math><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>n</mi><mn>0</mn></mrow></msub><mo>)</mo></math></span> converging to <span><math><mo>(</mo><mi>f</mi><mo>,</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span> in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>)</mo><mo>×</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span>, we prove the convergence of the solutions <span><math><mo>(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> of the Lagrange multiplier problem to the solution of the limit problem, when we let <span><math><mi>n</mi><mo>→</mo><mo>∞</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129746"},"PeriodicalIF":1.2,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222398","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}