Mouad Allalou, Mohamed El Ouaarabi, Abderrahmane Raji
{"title":"Existence and uniqueness results for a class of obstacle problem via Young’s measure theory","authors":"Mouad Allalou, Mohamed El Ouaarabi, Abderrahmane Raji","doi":"10.1007/s13324-024-00972-5","DOIUrl":null,"url":null,"abstract":"<div><p>The purpose of this article is to prove the existence and uniqueness of weak solutions to the following obstacle problem of <i>p</i>-Laplace-type: </p><div><div><span>$$\\begin{aligned} \\displaystyle \\int _{\\Omega }\\sigma _1(z,Du-\\mathcal {F}(u)):D(v-u)+\\sigma _2(z,Du):(v-u)+ \\left\\langle u\\vert u\\vert ^{p-2}, v- u\\right\\rangle \\mathrm {~d}z\\ge 0, \\end{aligned}$$</span></div></div><p>with data belonging to the dual of Sobolev spaces. The main result is demonstrated by means of Kinderlehrer and Stampacchia’s Theorem and Young’s measure theory.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-024-00972-5","RegionNum":3,"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
Abstract
The purpose of this article is to prove the existence and uniqueness of weak solutions to the following obstacle problem of p-Laplace-type:
with data belonging to the dual of Sobolev spaces. The main result is demonstrated by means of Kinderlehrer and Stampacchia’s Theorem and Young’s measure theory.
本文旨在证明以下p-拉普拉斯型障碍问题弱解的存在性和唯一性: $$\begin{aligned}\displaystyle int _{\Omega }\sigma _1(z,Du-\mathcal {F}(u)):D(v-u)+\sigma _2(z,Du):(v-u)+\left\langle u\vert u\vert ^{p-2}, v- u\right\rangle \mathrm {~d}z\ge 0, \end{aligned}$$with data belonging to the dual of Sobolev spaces.主要结果是通过金德勒和斯坦帕奇亚定理以及杨的度量理论证明的。
期刊介绍:
Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.