Existence and uniqueness results for a class of obstacle problem via Young’s measure theory

IF 1.4 3区 数学 Q1 MATHEMATICS
Mouad Allalou, Mohamed El Ouaarabi, Abderrahmane Raji
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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:

$$\begin{aligned} \displaystyle \int _{\Omega }\sigma _1(z,Du-\mathcal {F}(u)):D(v-u)+\sigma _2(z,Du):(v-u)+ \left\langle u\vert u\vert ^{p-2}, v- u\right\rangle \mathrm {~d}z\ge 0, \end{aligned}$$

with data belonging to the dual of Sobolev spaces. The main result is demonstrated by means of Kinderlehrer and Stampacchia’s Theorem and Young’s measure theory.

通过杨氏量纲理论求一类障碍问题的存在性和唯一性结果
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Analysis and Mathematical Physics
Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.70
自引率
0.00%
发文量
122
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.
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