EXISTENCE RESULTS IN WEIGHTED SOBOLEV SPACE FOR QUASILINEAR DEGENERATE P(Z)−ELLIPTIC PROBLEMS WITH A HARDY POTENTIAL

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-21 DOI:10.3846/mma.2024.18696

Ghizlane Zineddaine, Abdelaziz Sabiry, Said Melliani, Abderrezak Kassidi

引用次数: 0

Abstract

The objective of this work is to establish the existence of entropy solutions to degenerate nonlinear elliptic problems for $L^1$-data $f$ with a Hardy potential, in weighted Sobolev spaces with variable exponent, which are represented as follows \begin{gather*} -\text{div}\big(\Phi(z,v,\nabla v)\big)+g(z,v,\nabla v)=f+\rho\frac{\vert v \vert^{p(z)-2}v}{|v|^{p(z)}}, \end{gather*} where $-\text{div}(\Phi(z,v,\nabla v))$ is a Leray-Lions operator from $W_{0}^{1,p(z)}(\Omega,\omega)$ into its dual, $g(z,v,\nabla v)$ is a non-linearity term that only meets the growth condition, and $\rho>0$ is a constant.

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具有硬势的准线性退化 p(z)-椭圆问题在加权索波列夫空间中的存在结果

这项工作的目的是在具有可变指数的加权 Sobolev 空间中，为具有 Hardy 势的 $L^1$ 数据 $f$ 的退化非线性椭圆问题建立熵解的存在性，这些熵解表示如下：begin{gather*}-\text{div}\big(\Phi(z,v,\nabla v)\big)+g(z、v,\nabla v)=f+\rho\frac\vert v \vert^{p(z)-2}v}{|v|^{p(z)}},\end{gather*} 其中 $-\text{div}(\Phi(z,v,\nabla v))$ 是来自 $W_{0}^{1、p(z)}(\Omega,\omega)$ 到它的对偶，$g(z,v,\nabla v)$ 是一个只满足增长条件的非线性项，$\rho>0$ 是一个常数。

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

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.