Ghizlane Zineddaine, Abdelaziz Sabiry, Said Melliani, Abderrezak Kassidi
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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.
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.