Journal of Differential Equations最新文献

筛选
英文 中文
Simultaneous uniqueness and numerical inversion for an inverse problem in a coupled diffusion system 耦合扩散系统反问题的同时唯一性与数值反演
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-10-10 DOI: 10.1016/j.jde.2025.113827
Zhiyuan Li , Chunlong Sun
{"title":"Simultaneous uniqueness and numerical inversion for an inverse problem in a coupled diffusion system","authors":"Zhiyuan Li ,&nbsp;Chunlong Sun","doi":"10.1016/j.jde.2025.113827","DOIUrl":"10.1016/j.jde.2025.113827","url":null,"abstract":"<div><div>In this work, we investigate an inverse problem in determining multiple coefficients in a coupled diffusion system arising from the time-domain diffuse optical tomography with fluorescence. We simultaneously recover the distribution of the background absorption coefficient, photon diffusion coefficient, and fluorescence absorption in biological tissue by time-dependent boundary measurements. We build the uniqueness theorem for this multiple coefficients simultaneous inverse problem. After that, the numerical inversions for non-smooth absorption featuring various shaped inclusions are considered.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113827"},"PeriodicalIF":2.3,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268970","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
To what extent does the consideration of positive total flux influence the dynamics of Keller–Segel-type models? 正总通量的考虑在多大程度上影响了keller - segel型模型的动力学?
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-10-09 DOI: 10.1016/j.jde.2025.113808
Khadijeh Baghaei , Silvia Frassu , Yuya Tanaka , Giuseppe Viglialoro
{"title":"To what extent does the consideration of positive total flux influence the dynamics of Keller–Segel-type models?","authors":"Khadijeh Baghaei ,&nbsp;Silvia Frassu ,&nbsp;Yuya Tanaka ,&nbsp;Giuseppe Viglialoro","doi":"10.1016/j.jde.2025.113808","DOIUrl":"10.1016/j.jde.2025.113808","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Since the introduction of the Keller-Segel model in 1970 to describe chemotaxis (the interactions between cell distributions &lt;em&gt;u&lt;/em&gt; and chemical distributions &lt;em&gt;v&lt;/em&gt;), there has been a significant proliferation of research articles exploring various extensions and modifications of this model within the scientific community. From a technical standpoint, the totality of results concerning these variants are characterized by the assumption that the total flux, involving both distributions, of the model under consideration is &lt;em&gt;zero&lt;/em&gt;. This research aims to present a novel perspective by focusing on models with a &lt;em&gt;positive&lt;/em&gt; total flux. Specifically, by employing Robin-type boundary conditions for &lt;em&gt;u&lt;/em&gt; and &lt;em&gt;v&lt;/em&gt;, we seek to gain insights into the interactions between cells and their environment, uncovering important dynamics such as how variations in boundary conditions influence chemotactic behavior. In particular, the choice of the boundary conditions is motivated by real-world phenomena and by the fact that the related analysis reveals some interesting properties of the system.&lt;/div&gt;&lt;div&gt;Mathematically, or &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; we investigate Keller–Segel-type models with positive total flux &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, reading as&lt;span&gt;&lt;span&gt;&lt;span&gt;(⊕)&lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt;in&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mtext&gt;max&lt;/mtext&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt;in&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mtext&gt;max&lt;/mtext&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt;on&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mtext&gt;max&lt;/mtext&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113808"},"PeriodicalIF":2.3,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268973","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
Variational principles of invariance entropy dimension 不变熵维的变分原理
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-10-09 DOI: 10.1016/j.jde.2025.113819
Hu Chen , Yu Huang , Xingfu Zhong
{"title":"Variational principles of invariance entropy dimension","authors":"Hu Chen ,&nbsp;Yu Huang ,&nbsp;Xingfu Zhong","doi":"10.1016/j.jde.2025.113819","DOIUrl":"10.1016/j.jde.2025.113819","url":null,"abstract":"<div><div>We introduce two types of invariance entropy dimensions (<em>α</em>-invariance entropies), measure-theoretic invariance entropy dimensions (measure-theoretic <em>α</em>-invariance entropies), and measure-theoretic local invariance entropy dimensions (measure-theoretic local <em>α</em>-invariance entropy) to investigate the complexity of a control system with zero invariance entropy, where <span><math><mi>α</mi><mo>∈</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>. Under some reasonable assumptions, we respectively present two variational principles and inverse variational principles for <em>α</em>-invariance entropies and invariance entropy dimensions, and show that Bowen <em>α</em>-invariance entropy (Bowen invariance entropy dimension) and packing <em>α</em>-invariance entropy (packing invariance entropy dimension) can be determined via the corresponding local entropies of measures.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113819"},"PeriodicalIF":2.3,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270307","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 limit for a dispersion-managed NLS 色散管理NLS的大规模限制
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-10-09 DOI: 10.1016/j.jde.2025.113830
Jason Murphy
{"title":"Large scale limit for a dispersion-managed NLS","authors":"Jason Murphy","doi":"10.1016/j.jde.2025.113830","DOIUrl":"10.1016/j.jde.2025.113830","url":null,"abstract":"<div><div>We derive the standard power-type NLS as a scaling limit of the Gabitov–Turitsyn dispersion-managed NLS, using the 2<em>d</em> defocusing, cubic equation as a model case. In particular, we obtain global-in-time scattering solutions to the dispersion-managed NLS for large scale data of arbitrary <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"448 ","pages":"Article 113830"},"PeriodicalIF":2.3,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145262744","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
Multiple solutions for the nonlinear Schrödinger-Poisson system with a partial confinement 具有部分约束的非线性Schrödinger-Poisson系统的多解
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-10-08 DOI: 10.1016/j.jde.2025.113815
Liying Shan , Wei Shuai , Jianghua Ye
{"title":"Multiple solutions for the nonlinear Schrödinger-Poisson system with a partial confinement","authors":"Liying Shan ,&nbsp;Wei Shuai ,&nbsp;Jianghua Ye","doi":"10.1016/j.jde.2025.113815","DOIUrl":"10.1016/j.jde.2025.113815","url":null,"abstract":"<div><div>We study the following nonlinear Schrödinger-Poisson system with a partial confinement<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mo>(</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo><mi>u</mi><mo>+</mo><mi>λ</mi><mi>ϕ</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>u</mi><mo>=</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>ϕ</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>p</mi><mo>∈</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></span> and <span><math><mi>λ</mi><mo>&gt;</mo><mn>0</mn></math></span> is a parameter. The existence and nonexistence results are established by variational methods, depending on the parameters <em>p</em> and <em>λ</em>. It turns out that <span><math><mi>p</mi><mo>=</mo><mn>3</mn></math></span> is a critical value for the existence of solutions.</div><div>Our results can be viewed as an extension of the results of Ruiz <span><span>[33]</span></span> concerning the nonlinear Schrödinger-Poisson equation with a positive constant potential. However, due to the presence of partial confinement, the Nehari-Pohozaev manifold method is no longer applicable in this paper for <span><math><mi>p</mi><mo>∈</mo><mo>(</mo><mn>3</mn><mo>,</mo><mfrac><mrow><mn>16</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>]</mo></math></span>. We need to explore the more complicated underlying functional geometry with a different variational approach. Moreover, we also construct saddle type nodal solutions whose nodal domains meet at the origin.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"451 ","pages":"Article 113815"},"PeriodicalIF":2.3,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266163","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 a scaled abstract linking theorem with an application to the Schrödinger–Poisson–Slater equation 缩放抽象连接定理及其在Schrödinger-Poisson-Slater方程中的应用
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-10-08 DOI: 10.1016/j.jde.2025.113824
Kanishka Perera , Kaye Silva
{"title":"On a scaled abstract linking theorem with an application to the Schrödinger–Poisson–Slater equation","authors":"Kanishka Perera ,&nbsp;Kaye Silva","doi":"10.1016/j.jde.2025.113824","DOIUrl":"10.1016/j.jde.2025.113824","url":null,"abstract":"<div><div>We prove an abstract linking theorem that can be used to show existence of solutions to various types of variational elliptic equations, including Schrödinger–Poisson–Slater type equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113824"},"PeriodicalIF":2.3,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145236433","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 existence of weak solutions to a Baer–Nunziato type system 一类Baer-Nunziato型系统弱解的存在性
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-10-08 DOI: 10.1016/j.jde.2025.113804
Martin Kalousek, Šárka Nečasová
{"title":"On existence of weak solutions to a Baer–Nunziato type system","authors":"Martin Kalousek,&nbsp;Šárka Nečasová","doi":"10.1016/j.jde.2025.113804","DOIUrl":"10.1016/j.jde.2025.113804","url":null,"abstract":"<div><div>In this paper, we consider a compressible one velocity Baer–Nunziato type system with dissipation describing the evolution of a mixture of two compressible heat conducting fluids. The complete existence proof for weak solutions to this system was addressed as an open problem in <span><span>[12, Section 5]</span></span>. The purpose of this paper is to prove the global in time existence of weak solutions to the one velocity Baer–Nunziato type system for arbitrary large initial data. The goal is achieved in three steps. Firstly, the given system is transformed into a new one which possesses the “Navier-Stokes-Fourier” structure. Secondly, the new system is solved by an adaptation of the Feireisl–Lions approach for solving the compressible full system applying also the almost compactness property introduced by Vasseur et al. <span><span>[19]</span></span>. Finally, the existence of a weak solution to the original one velocity Baer–Nunziato system is shown using the almost uniqueness property of renormalized solutions to pure transport equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"452 ","pages":"Article 113804"},"PeriodicalIF":2.3,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268971","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
Harmonic mappings on Grushin planes Grushin平面上的调和映射
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-10-08 DOI: 10.1016/j.jde.2025.113806
Tomasz Adamowicz , Marcin Walicki , Ben Warhurst
{"title":"Harmonic mappings on Grushin planes","authors":"Tomasz Adamowicz ,&nbsp;Marcin Walicki ,&nbsp;Ben Warhurst","doi":"10.1016/j.jde.2025.113806","DOIUrl":"10.1016/j.jde.2025.113806","url":null,"abstract":"<div><div>We study the Grushin spaces given by Hölder regular vector fields with the Carnot–Carathéodory distance, equipped with the natural weighted <em>n</em>-Lebesgue measure. It turns out that such a measure is <em>n</em>-Ahlfors regular and <em>p</em>-Muckenhoupt for <span><math><mi>p</mi><mo>&gt;</mo><mn>1</mn></math></span>. We investigate the related 2-Dirichlet energy and the harmonic mappings, and focus our attention on harmonic functions and mappings from domains in a Grushin plane to Euclidean spaces <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>, for <span><math><mi>m</mi><mo>≥</mo><mn>1</mn></math></span>. Our results enclose the second order Sobolev regularity, the Bochner identity and its consequences for the regularity of harmonic mappings, the Liouville-type theorems and a counterpart of the Lewy theorem. Furthermore, the Korevaar–Schoen energy of mappings on Grushin planes is studied and proven to be equivalent to the 2-Dirichlet energy. The discussion is illustrated by several examples.</div><div>We generalize some geometric and regularity results by Ferrari–Valdinoci <span><span>[23]</span></span> and Franchi–Serapioni <span><span>[30]</span></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113806"},"PeriodicalIF":2.3,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269783","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 application of the Ważewski principle to the characterization of continuous probability distributions Ważewski原理在连续概率分布表征中的应用
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-10-08 DOI: 10.1016/j.jde.2025.113817
Mariusz Bieniek
{"title":"An application of the Ważewski principle to the characterization of continuous probability distributions","authors":"Mariusz Bieniek","doi":"10.1016/j.jde.2025.113817","DOIUrl":"10.1016/j.jde.2025.113817","url":null,"abstract":"<div><div>We introduce an unexpected application of the Ważewski retract principle to a probabilistic challenge: identifying probability distributions via the regression function of ordered statistical data such as order statistics and record values. In order to prevent repetitive arguments across various models, we examine a wide-ranging category of models known as generalized order statistics. We establish a precise formula for the underlying distribution using a specified regression and a solution to an additional Volterra-Stieltjes integral equation. Moreover, we identify the class of feasible regression functions by determining the necessary and sufficient conditions for a function to qualify as a regression. Our findings are supported by examples that highlight the importance of the stipulated conditions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113817"},"PeriodicalIF":2.3,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270305","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
Fractional De Giorgi conjecture in dimension 2 via complex-plane methods 基于复平面方法的二维分数阶De Giorgi猜想
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-10-07 DOI: 10.1016/j.jde.2025.113816
Serena Dipierro , João Gonçalves da Silva , Giorgio Poggesi , Enrico Valdinoci
{"title":"Fractional De Giorgi conjecture in dimension 2 via complex-plane methods","authors":"Serena Dipierro ,&nbsp;João Gonçalves da Silva ,&nbsp;Giorgio Poggesi ,&nbsp;Enrico Valdinoci","doi":"10.1016/j.jde.2025.113816","DOIUrl":"10.1016/j.jde.2025.113816","url":null,"abstract":"<div><div>We provide a new proof of the fractional version of the De Giorgi conjecture for the Allen-Cahn equation in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> for the full range of exponents. Our proof combines a method introduced by A. Farina in 2003 with the <em>s</em>-harmonic extension of the fractional Laplacian in the half-space <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> introduced by L. Caffarelli and L. Silvestre in 2007.</div><div>We also provide a representation formula for finite-energy weak solutions of a class of weighted elliptic partial differential equations in the half-space <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup></math></span> under Neumann boundary conditions. This generalizes the <em>s</em>-harmonic extension of the fractional Laplacian and allows us to relate a general problem in the extended space with a nonlocal problem on the trace.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113816"},"PeriodicalIF":2.3,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270306","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
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信