Year: 2021
Author: Adil Abbassi, Chakir Allalou, Abderrazak Kassidi
Journal of Mathematical Study, Vol. 54 (2021), Iss. 4 : pp. 337–356
Abstract
In this paper, we are concerned with a show the existence of a entropy solution to the obstacle problem associated with the equation of the type :
$\begin{cases} Au+g(x,u,∇u) = f & {\rm in} & Ω \\ u=0 & {\rm on} & ∂Ω \end{cases}$
where $\Omega$ is a bounded open subset of $\;\mathbb{R}^{N}$, $N\geq 2$, $A\,$ is an operator of Leray-Lions type acting from $\; W_{0}^{1,\overrightarrow{p}(.)} (\Omega,\ \overrightarrow{w}(.))\;$ into its dual $\; W_{0}^{-1,\overrightarrow{p}'(.)} (\Omega,\ \overrightarrow{w}^*(.))$ and $\,L^1\,-\,$deta. The nonlinear term $\;g\,$: $\Omega\times \mathbb{R}\times \mathbb{R}^{N}\longrightarrow \mathbb{R} $ satisfying only some growth condition.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v54n4.21.01
Journal of Mathematical Study, Vol. 54 (2021), Iss. 4 : pp. 337–356
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Entropy solutions Anisotropic elliptic equations weighted anisotropic variable exponent Sobolev space.