{"title":"无界域上$\\protect \\overrightarrow {p(x)}$各向异性椭圆方程","authors":"Ahmed Aberqi, Benali Aharrouch, Jaouad Bennouna","doi":"10.1007/s40306-021-00434-1","DOIUrl":null,"url":null,"abstract":"<div><p>We study a class of nonlinear elliptic problems with Dirichlet conditions in the framework of the Sobolev anisotropic spaces with variable exponent, involving an anisotropic operator on an unbounded domain <span>\\({\\varOmega }\\subset \\mathbb {R}^{N} (N \\geq 2)\\)</span>. We prove the existence of entropy solutions avoiding sign condition and coercivity on the lower order terms.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40306-021-00434-1","citationCount":"0","resultStr":"{\"title\":\"On Some \\\\(\\\\protect \\\\overrightarrow {p(x)}\\\\) Anisotropic Elliptic Equations in Unbounded Domain\",\"authors\":\"Ahmed Aberqi, Benali Aharrouch, Jaouad Bennouna\",\"doi\":\"10.1007/s40306-021-00434-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study a class of nonlinear elliptic problems with Dirichlet conditions in the framework of the Sobolev anisotropic spaces with variable exponent, involving an anisotropic operator on an unbounded domain <span>\\\\({\\\\varOmega }\\\\subset \\\\mathbb {R}^{N} (N \\\\geq 2)\\\\)</span>. We prove the existence of entropy solutions avoiding sign condition and coercivity on the lower order terms.</p></div>\",\"PeriodicalId\":45527,\"journal\":{\"name\":\"Acta Mathematica Vietnamica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-07-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40306-021-00434-1\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Vietnamica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40306-021-00434-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Vietnamica","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40306-021-00434-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
On Some \(\protect \overrightarrow {p(x)}\) Anisotropic Elliptic Equations in Unbounded Domain
We study a class of nonlinear elliptic problems with Dirichlet conditions in the framework of the Sobolev anisotropic spaces with variable exponent, involving an anisotropic operator on an unbounded domain \({\varOmega }\subset \mathbb {R}^{N} (N \geq 2)\). We prove the existence of entropy solutions avoiding sign condition and coercivity on the lower order terms.
期刊介绍:
Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.