带有加权非局部源和梯度吸收项的准线性椭圆微分不等式的利乌维尔类型定理

IF 2.1 2区数学 Q1 MATHEMATICS Calculus of Variations and Partial Differential Equations Pub Date : 2024-09-16 DOI:10.1007/s00526-024-02821-6

Ye Du, Zhong Bo Fang

{"title":"带有加权非局部源和梯度吸收项的准线性椭圆微分不等式的利乌维尔类型定理","authors":"Ye Du, Zhong Bo Fang","doi":"10.1007/s00526-024-02821-6","DOIUrl":null,"url":null,"abstract":"This work is concerned with the nonexistence of nontrivial nonnegative weak solutions for a strongly p-coercive elliptic differential inequality with weighted nonlocal source and gradient absorption terms in the whole space. Under the condition that the positive weight in the absorption term is either a sufficiently small constant or more general, we establish new Liouville type results containing the critical case. The key ingredient in the proof is the rescaled test function method developed by Mitidieri and Pohozaev.","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":"2 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Liouville type theorems for a quasilinear elliptic differential inequality with weighted nonlocal source and gradient absorption terms\",\"authors\":\"Ye Du, Zhong Bo Fang\",\"doi\":\"10.1007/s00526-024-02821-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work is concerned with the nonexistence of nontrivial nonnegative weak solutions for a strongly p-coercive elliptic differential inequality with weighted nonlocal source and gradient absorption terms in the whole space. Under the condition that the positive weight in the absorption term is either a sufficiently small constant or more general, we establish new Liouville type results containing the critical case. The key ingredient in the proof is the rescaled test function method developed by Mitidieri and Pohozaev.\",\"PeriodicalId\":9478,\"journal\":{\"name\":\"Calculus of Variations and Partial Differential Equations\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Calculus of Variations and Partial Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00526-024-02821-6\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Calculus of Variations and Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00526-024-02821-6","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本研究关注的是在整个空间中具有加权非局部源和梯度吸收项的强 p 胁迫椭圆微分不等式的非微不足道的非负弱解的不存在性。在吸收项中的正权重为足够小的常数或更一般的条件下，我们建立了包含临界情况的新的柳维尔类型结果。证明的关键要素是米蒂迪埃里和波霍扎耶夫开发的重标检验函数方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Liouville type theorems for a quasilinear elliptic differential inequality with weighted nonlocal source and gradient absorption terms

This work is concerned with the nonexistence of nontrivial nonnegative weak solutions for a strongly p-coercive elliptic differential inequality with weighted nonlocal source and gradient absorption terms in the whole space. Under the condition that the positive weight in the absorption term is either a sufficiently small constant or more general, we establish new Liouville type results containing the critical case. The key ingredient in the proof is the rescaled test function method developed by Mitidieri and Pohozaev.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.

期刊最新文献

The rigidity of minimal Legendrian submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices Isoperimetry and the properness of weak inverse mean curvature flow Hele-Shaw flow as a singular limit of a Keller-Segel system with nonlinear diffusion On the $$L^{p}$$ dual Minkowski problem for $$-1<0$$ Convergence of semi-convex functions in CAT(1)-spaces