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

IF 1.6 3区 数学 Q1 MATHEMATICS
Ghizlane Zineddaine, Abdelaziz Sabiry, Said Melliani, Abderrezak Kassidi
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引用次数: 0

摘要

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。
EXISTENCE RESULTS IN WEIGHTED SOBOLEV SPACE FOR QUASILINEAR DEGENERATE P(Z)−ELLIPTIC PROBLEMS WITH A HARDY POTENTIAL
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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来源期刊
CiteScore
2.80
自引率
5.60%
发文量
28
审稿时长
4.5 months
期刊介绍: Mathematical Modelling and Analysis publishes original research on all areas of mathematical modelling and analysis.
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