Journal of Mathematical Analysis and Applications最新文献

{"title":"Regularity for solutions of parabolic equations with anisotropic growth","authors":"Shuang Liang,&nbsp;Xuedan Zhao,&nbsp;Xinyue Zhai","doi":"10.1016/j.jmaa.2025.130041","DOIUrl":"10.1016/j.jmaa.2025.130041","url":null,"abstract":"<div><div>We prove the integrability for solutions of the nonlinear parabolic problem with anisotropic growth<span><span><span><math><mrow><mrow><mo>{</mo><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></munderover><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>D</mi><mi>u</mi><mo>)</mo><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mspace></mspace><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mspace></mspace><msub><mrow><mi>Q</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>=</mo><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>0</mn><mspace></mspace><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mspace></mspace><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>0</mn><mspace></mspace><mspace></mspace></mtd><mtd><mtext>on</mtext><mspace></mspace><mspace></mspace><mi>Γ</mi><mo>=</mo><mo>∂</mo><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></mtd></mtr></mtable></mrow></mrow></math></span></span></span> for the model case of <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>ξ</mi><mo>)</mo><mo>≈</mo><mo>|</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>i</mi></mrow></msub><msup><mrow><mo>|</mo></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>−</mo><mn>2</mn></mrow></msup><msub><mrow><mi>ξ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>&gt;</mo><mn>1</mn></math></span> for <span><math><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>n</mi></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130041"},"PeriodicalIF":1.2,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049178","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":"Weak fixed point property of order p with respect to orbits","authors":"Halimeh Ardakani ,&nbsp;Kamal Fallahi","doi":"10.1016/j.jmaa.2025.130044","DOIUrl":"10.1016/j.jmaa.2025.130044","url":null,"abstract":"<div><div>In this note, weakly <em>p</em>-summable (resp. weakly <em>p</em>-summable and Dunford-Pettis) sequences in a Banach space are used to obtain a characterization of weak normal structure of order <em>p</em> (resp. Right normal structure of order <em>p</em>). It is proved that a Banach space has weak normal structure of order <em>p</em> (resp. Right normal structure of order <em>p</em>) if and only if it has the weak fixed point property of order <em>p</em> (resp. Right fixed point property of order <em>p</em>) for non-expansive mappings with respect to orbits.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130044"},"PeriodicalIF":1.2,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049181","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":"Robust and minimum norm partial eigenvalue assignment in singular vibration systems","authors":"Kang Zhao,&nbsp;Jiantian Wang,&nbsp;Fangting Deng","doi":"10.1016/j.jmaa.2025.130048","DOIUrl":"10.1016/j.jmaa.2025.130048","url":null,"abstract":"<div><div>In this paper, the partial quadratic eigenvalue assignment problem (PQEAP) for the singular second-order system by the acceleration-velocity-displacement active controller was considered. Based on the spectral decomposition of quadratic symmetric pencil, a sufficient and necessary condition of the closed-loop to preserve no spill-over is provided. Using the receptances and system matrices, the parametric solutions of the PQEAP are characterized. Finally, a gradient-based optimization algorithm for the robust and minimum norm solution of the PQEAP is proposed. Numerical examples show the robustness and effectiveness of the proposed method.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130048"},"PeriodicalIF":1.2,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099371","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":"Hamilton inequality for the p-Laplacian on weighted graphs with the CDp⋅(m,K) curvature","authors":"Yongtao Liu","doi":"10.1016/j.jmaa.2025.130036","DOIUrl":"10.1016/j.jmaa.2025.130036","url":null,"abstract":"<div><div>In this paper, we study Hamilton type gradient estimates for the <em>p</em>-Laplacian on weighted graphs. For <span><math><mi>p</mi><mo>&gt;</mo><mn>5</mn></math></span> and some additional assumptions, we derive a more general gradient estimate of Hamilton type for positive solutions to the <em>p</em>-Laplacian heat equation on finite graphs satisfying the <span><math><mi>C</mi><msubsup><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow><mrow><msqrt><mrow><mo>⋅</mo></mrow></msqrt></mrow></msubsup><mo>(</mo><mi>m</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span> curvature. The analogous result is also proved for locally finite graphs with bounded weighted vertex degree. As an application of our main results, we show that the corresponding Harnack inequality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130036"},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997594","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 approximate solution of a perturbed Fokker-Planck equation","authors":"Yan Luo ,&nbsp;Kaicheng Sheng","doi":"10.1016/j.jmaa.2025.130040","DOIUrl":"10.1016/j.jmaa.2025.130040","url":null,"abstract":"<div><div>This paper focuses on finding an approximate solution of a kind of Fokker-Planck equation with time-dependent perturbations. A formulation of the approximate solution of the equation is constructed, and then the existence of the formulation is proved. The related Hamiltonian dynamical system explains the estimations. Examples of the Ornstein-Uhlenbeck process model and the nonlinear Langevin equation are used to validate the proposed results. Our work provides a more comprehensive understanding of the long-time behaviour of systems described by this Fokker-Planck equation and the corresponding stochastic differential equation.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130040"},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049970","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":"Non-invertible mappings of linear PDEs to nonlinear PDEs through the symmetry-based method","authors":"Subhankar Sil ,&nbsp;George Bluman","doi":"10.1016/j.jmaa.2025.130038","DOIUrl":"10.1016/j.jmaa.2025.130038","url":null,"abstract":"<div><div>We show that the well-known Hopf–Cole transformation mapping the linear heat equation to the nonlinear Burgers' equation naturally extends to the mapping of any linear PDE to a non-invertibly equivalent nonlinear PDE. This mapping is obtained through the symmetry-based method by using the admitted obvious scaling symmetry in the dependent variable of any linear homogeneous PDE. Furthermore, each nontrivial point symmetry of any linear PDE yields a corresponding nonlocally related nonlinear PDE. The mapping relating the linear PDE and the corresponding nonlinear PDE is not one-to-one. As examples we consider the linear heat equation, the linear wave equation, Laplace's equation and the Helmholtz equation in two or more independent variables. We exhibit some exact solutions of the corresponding nonlinear system of PDEs from a known solution of the associated linear PDE. Moreover, we find nonlocal symmetries for the corresponding nonlocally related nonlinear systems of PDEs through the commutator relationship between point symmetries of the associated linear PDE.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130038"},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027480","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":"The complex structure of the Teichmüller space of circle diffeomorphisms in the Zygmund smooth class II","authors":"Katsuhiko Matsuzaki","doi":"10.1016/j.jmaa.2025.130035","DOIUrl":"10.1016/j.jmaa.2025.130035","url":null,"abstract":"<div><div>In our previous paper with the same title, we established the complex Banach manifold structure for the Teichmüller space of circle diffeomorphisms whose derivatives belong to the Zygmund class. This was achieved by demonstrating that the Schwarzian derivative map is a holomorphic split submersion. We also obtained analogous results for the pre-Schwarzian derivative map. In this second part of the study, we investigate the structure of the image of the pre-Schwarzian derivative map, viewing it as a fiber space over the Bers embedding of the Teichmüller space, and prove that it forms a real-analytic disk-bundle. Furthermore, we consider the little Zygmund class and establish corresponding results for the closed Teichmüller subspace consisting of mappings in this class. Finally, we construct the quotient space of this subspace in analogy with the asymptotic Teichmüller space and prove that the quotient Bers embedding and pre-Bers embedding are well-defined and injective, thereby endowing it with a complex structure modeled on a quotient Banach space.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130035"},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049182","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":"Wolff potential estimates for elliptic double obstacle problems with Orlicz growth","authors":"Qi Xiong ,&nbsp;Zhenqiu Zhang ,&nbsp;Lingwei Ma","doi":"10.1016/j.jmaa.2025.130034","DOIUrl":"10.1016/j.jmaa.2025.130034","url":null,"abstract":"<div><div>In this paper, we consider the solutions of the elliptic double obstacle problems with Orlicz growth involving measure data. Some pointwise estimates for the approximable solutions to these problems are obtained in terms of fractional maximal operators. Furthermore, we establish pointwise and oscillation estimates for the gradients of solutions via the nonlinear Wolff potentials, which in turn yield <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span>-regularity of solutions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130034"},"PeriodicalIF":1.2,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010784","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":"The compactness of Trudinger-Moser type functionals with variable exponents for domains in RN","authors":"Masato Hashizume,&nbsp;Michinori Ishiwata,&nbsp;Xu Yan","doi":"10.1016/j.jmaa.2025.130037","DOIUrl":"10.1016/j.jmaa.2025.130037","url":null,"abstract":"<div><div>In this paper, we consider the compactness property of several Trudinger-Moser type functionals with variable exponents. We establish various nearly optimal conditions on the variable exponents which assure the compactness or the noncompactness of functionals. We treat this problem both on bounded domains and the entire domain. The entire domain case needs the condition which excludes the so-called vanishing phenomena which has not been well treated so far together with the consideration of the concentration phenomena.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130037"},"PeriodicalIF":1.2,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027481","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":"Positive singular solutions of a certain elliptic PDE","authors":"Negar Mohammadnejad","doi":"10.1016/j.jmaa.2025.130033","DOIUrl":"10.1016/j.jmaa.2025.130033","url":null,"abstract":"<div><div>In this paper, we investigate the existence of positive singular solutions for a system of partial differential equations on a bounded domain<span><span><span>(1)</span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>κ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>|</mo><mi>∇</mi><mi>v</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mspace></mspace><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>﹨</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>,</mo></mtd></mtr><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>v</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>κ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mspace></mspace><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>﹨</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mi>v</mi><mo>=</mo><mn>0</mn><mspace></mspace></mtd><mtd><mtext>on</mtext><mspace></mspace><mspace></mspace><mo>∂</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>.</mo></mtd></mtr></mtable></mrow></math></span></span></span> We investigate the existence of positive singular solutions within <span><math><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, the unit ball centered at the origin in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, under the conditions <span><math><mi>N</mi><mo>≥</mo><mn>3</mn></math></span> and <span><math><mfrac><mrow><mi>N</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mn>2</mn></math></span>. Additionally, we assume that <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are non-negative, continuous functions satisfying <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><msub><mrow><mi>κ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>0</mn></math></span>. Our system is an extension of the PDE studied by Aghajani et al. <span><span>[1]</span></span> under similar assumptions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130033"},"PeriodicalIF":1.2,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010783","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}