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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-11-02 DOI:10.1007/s13324-024-00972-5

Mouad Allalou, Mohamed El Ouaarabi, Abderrahmane Raji

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引用次数: 0

摘要

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。

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

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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.