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Second order regularity for solutions to anisotropic degenerate elliptic equations
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-24 DOI: 10.1016/j.jde.2025.113250
Daniel Baratta, Luigi Muglia, Domenico Vuono
{"title":"Second order regularity for solutions to anisotropic degenerate elliptic equations","authors":"Daniel Baratta,&nbsp;Luigi Muglia,&nbsp;Domenico Vuono","doi":"10.1016/j.jde.2025.113250","DOIUrl":"10.1016/j.jde.2025.113250","url":null,"abstract":"<div><div>We consider solutions to degenerate anisotropic elliptic equations in order to study their regularity. In particular we establish second-order estimates and enclose regularity results for the stress field. All our results are new even in the euclidean case.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113250"},"PeriodicalIF":2.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683570","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 2D stochastic nonlinearly coupled fluid-structure interaction problem in compliant arteries with unrestricted structural displacement
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-24 DOI: 10.1016/j.jde.2025.113243
Krutika Tawri
{"title":"A 2D stochastic nonlinearly coupled fluid-structure interaction problem in compliant arteries with unrestricted structural displacement","authors":"Krutika Tawri","doi":"10.1016/j.jde.2025.113243","DOIUrl":"10.1016/j.jde.2025.113243","url":null,"abstract":"<div><div>In this paper, we study a nonlinear fluid-structure interaction (FSI) problem driven by a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a 2D cylinder interacting with an elastic wall whose elastodynamics is described by membrane/shell equations. The stochastic force is applied both to the fluid equations as a volumetric body force, and to the structure as an external forcing to the deformable fluid boundary. The fluid and the structure are nonlinearly coupled via the kinematic and dynamic conditions assumed at the moving interface, which is a random variable not known a priori. Majority of the existing FSI literature builds on the assumption that the structure can only be deformed radially, neglecting its longitudinal displacement. In this article, we consider the case where the structure is allowed to have vectorial (unrestricted) deformations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"431 ","pages":"Article 113243"},"PeriodicalIF":2.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683313","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
Smoothing effects and maximal Hölder regularity for non-autonomous Kolmogorov equations in infinite dimension
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-24 DOI: 10.1016/j.jde.2025.113245
Sandra Cerrai , Alessandra Lunardi
{"title":"Smoothing effects and maximal Hölder regularity for non-autonomous Kolmogorov equations in infinite dimension","authors":"Sandra Cerrai ,&nbsp;Alessandra Lunardi","doi":"10.1016/j.jde.2025.113245","DOIUrl":"10.1016/j.jde.2025.113245","url":null,"abstract":"<div><div>We prove smoothing properties and optimal Schauder type estimates for a class of nonautonomous evolution equations driven by time dependent Ornstein-Uhlenbeck operators in a separable Hilbert space. They arise as Kolmogorov equations of linear nonautonomous stochastic differential equations with Gaussian noise.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113245"},"PeriodicalIF":2.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684983","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
Universal gradient estimates of Δu + a(x)up(ln⁡(u+c))q = 0 on complete Riemannian manifolds
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-24 DOI: 10.1016/j.jde.2025.113257
Chong Song, Jibo Wu
{"title":"Universal gradient estimates of Δu + a(x)up(ln⁡(u+c))q = 0 on complete Riemannian manifolds","authors":"Chong Song,&nbsp;Jibo Wu","doi":"10.1016/j.jde.2025.113257","DOIUrl":"10.1016/j.jde.2025.113257","url":null,"abstract":"<div><div>In this paper, we study the elliptic non-linear equation <span><math><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup><msup><mrow><mo>(</mo><mi>ln</mi><mo>⁡</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>c</mi><mo>)</mo><mo>)</mo></mrow><mrow><mi>q</mi></mrow></msup><mo>=</mo><mn>0</mn></math></span> on a complete Riemannian manifold with Ricci curvature bounded from below. By applying Nash-Moser iteration, we establish universal gradient estimates for positive solutions to the equation, where <span><math><mi>c</mi><mo>≥</mo><mn>1</mn></math></span> and <span><math><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is allowed to change sign. As an application, we obtain Liouville theorems when the manifold has non-negative Ricci curvature and <span><math><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is constant.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113257"},"PeriodicalIF":2.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684984","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 well-posedness of the minimum energy estimator for a defocusing cubic wave equation
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-22 DOI: 10.1016/j.jde.2025.113258
Jesper Schröder
{"title":"Local well-posedness of the minimum energy estimator for a defocusing cubic wave equation","authors":"Jesper Schröder","doi":"10.1016/j.jde.2025.113258","DOIUrl":"10.1016/j.jde.2025.113258","url":null,"abstract":"<div><div>This work is concerned with the <em>minimum energy estimator</em> for a nonlinear hyperbolic partial differential equation. The <em>Mortensen observer</em> – originally introduced for the energy-optimal reconstruction of the state of nonlinear finite-dimensional systems – is formulated for a disturbed cubic wave equation and the associated observer equation is derived. An in depth study of the associated optimal control problem and sensitivity analysis of the corresponding value function reveals that the energy optimal state estimator is well-defined. Deploying a classical fixed point argument we proceed to show that the observer equation is locally well-posed.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113258"},"PeriodicalIF":2.4,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683571","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
Backward stochastic Volterra integral equations with jumps and some related problems
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-21 DOI: 10.1016/j.jde.2025.113240
Zongkui Fu, Shasha Shen, Jinbiao Wu
{"title":"Backward stochastic Volterra integral equations with jumps and some related problems","authors":"Zongkui Fu,&nbsp;Shasha Shen,&nbsp;Jinbiao Wu","doi":"10.1016/j.jde.2025.113240","DOIUrl":"10.1016/j.jde.2025.113240","url":null,"abstract":"<div><div>In this paper, we deal with backward stochastic Volterra integral equations with jumps. Firstly, we present the well-posedness of backward stochastic Volterra integral equations with jumps in the sense of adapted M-solution. Secondly, we give some properties of backward stochastic Volterra integral equations with jumps, which contain the duality principle, comparison theorem and the regularity of adapted M-solution. Thirdly, dynamic risk measure by means of backward stochastic Volterra integral equations with jumps is established. Fourthly, a maximum principle of Pontryagin type is obtained for an optimal control problem of stochastic Volterra integral equations with jumps. Finally, we investigate the well-posedness of linear fractional backward stochastic Volterra integral equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113240"},"PeriodicalIF":2.4,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683569","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
Two classes of Benjamin–Ono-type equations with the Hilbert operator related to the Calogero–Moser system and the classical orthogonal polynomials
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-21 DOI: 10.1016/j.jde.2025.113249
Ling-Juan Yan , Ya-Jie Liu , Xing-Biao Hu , Ying-Nan Zhang
{"title":"Two classes of Benjamin–Ono-type equations with the Hilbert operator related to the Calogero–Moser system and the classical orthogonal polynomials","authors":"Ling-Juan Yan ,&nbsp;Ya-Jie Liu ,&nbsp;Xing-Biao Hu ,&nbsp;Ying-Nan Zhang","doi":"10.1016/j.jde.2025.113249","DOIUrl":"10.1016/j.jde.2025.113249","url":null,"abstract":"<div><div>This paper investigates two distinct classes of Benjamin–Ono(BO)-type equations with the Hilbert operator. The first class consists of equations with constant coefficients, derived from linear differential equations, with a specific focus on the Mikhailov–Novikov equation and Satsuma–Mimura equation. The second class involves BO-type equations with variable coefficients linked to orthogonal polynomials, including Hermite, Jacobi, and Laguerre polynomials. A key aspect of transforming these differential equations into BO-type equations is that the zeros of the polynomial or periodic solutions must lie in the upper half-plane. For linear and quadratic polynomials, we directly analyze their zeros to determine the solutions of corresponding BO-type equations. For higher-order polynomials, we use the pole expansion method to derive the governing many-body systems of the zeros. This study deepens our understanding of the relationship between the zeros of polynomials and the solutions of BO-type equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113249"},"PeriodicalIF":2.4,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685427","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 controllability of the Korteweg-de Vries equation with the right Dirichlet control
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-20 DOI: 10.1016/j.jde.2025.113235
Hoai-Minh Nguyen
{"title":"Local controllability of the Korteweg-de Vries equation with the right Dirichlet control","authors":"Hoai-Minh Nguyen","doi":"10.1016/j.jde.2025.113235","DOIUrl":"10.1016/j.jde.2025.113235","url":null,"abstract":"<div><div>The Korteweg-de Vries (KdV) equation with the right Dirichlet control is small time, locally, exactly controllable for all non-critical lengths and its linearized system is not controllable for <em>all</em> critical lengths. In this paper, we give a definitive picture of the local controllability properties of this control problem for all critical lengths. In particular, we show that the unreachable space of the linearized system is always of dimension 1 and the KdV system with the right Dirichlet control is not locally null controllable in small time for any critical length. We also give a criterion to determine whether the system is locally exactly controllable in finite time or <em>not</em> locally null controllable in any positive time for <em>all</em> critical lengths. Consequently, we show that there exist critical lengths such that the system is <em>not</em> locally null controllable in small time but is locally exactly controllable in finite time.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113235"},"PeriodicalIF":2.4,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683565","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
Global existence of strong solutions to the Landau–Lifshitz–Slonczewski equation
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-20 DOI: 10.1016/j.jde.2025.113242
Chenlu Zhang, Huaqiao Wang
{"title":"Global existence of strong solutions to the Landau–Lifshitz–Slonczewski equation","authors":"Chenlu Zhang,&nbsp;Huaqiao Wang","doi":"10.1016/j.jde.2025.113242","DOIUrl":"10.1016/j.jde.2025.113242","url":null,"abstract":"<div><div>In this paper, we focus on the existence of strong solutions for the Cauchy problem of the three-dimensional Landau-Lifshitz-Slonczewski equation. We construct a new combination of Bourgain space and Lebesgue space where linear and nonlinear estimates can be closed by applying frequency decomposition and energy methods. Finally, we establish the existence and uniqueness of the global strong solution provided that the initial data belongs to Besov space <span><math><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>˙</mo></mrow></mover></mrow><mrow><mi>Ω</mi></mrow><mrow><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msubsup></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113242"},"PeriodicalIF":2.4,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685426","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 Neumann problem for a class of Hessian quotient type equations
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2025-03-20 DOI: 10.1016/j.jde.2025.113251
Jiabao Gong, Zixuan Liu, Qiang Tu
{"title":"The Neumann problem for a class of Hessian quotient type equations","authors":"Jiabao Gong,&nbsp;Zixuan Liu,&nbsp;Qiang Tu","doi":"10.1016/j.jde.2025.113251","DOIUrl":"10.1016/j.jde.2025.113251","url":null,"abstract":"<div><div>In this paper, we consider the Neumann problem for a class of Hessian quotient equations involving a gradient term on the right-hand side in Euclidean space. More precisely, we derive the interior gradient estimates for the <span><math><mo>(</mo><mi>Λ</mi><mo>,</mo><mi>k</mi><mo>)</mo></math></span>-convex solution of Hessian quotient equation <span><math><mfrac><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>Λ</mi><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo><mo>)</mo></mrow><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>(</mo><mi>Λ</mi><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo><mo>)</mo></mrow></mfrac><mo>=</mo><mi>ψ</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>D</mi><mi>u</mi><mo>)</mo></math></span> with <span><math><mn>0</mn><mo>≤</mo><mi>l</mi><mo>&lt;</mo><mi>k</mi><mo>≤</mo><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msubsup></math></span> under the assumption of the growth condition. As an application, we obtain the global a priori estimates and the existence theorem for the Neumann problem of this Hessian quotient type equation.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"431 ","pages":"Article 113251"},"PeriodicalIF":2.4,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683312","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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