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Anisotropic Elliptic Nonlinear Obstacle Problem with Weighted Variable Exponent

Anisotropic Elliptic Nonlinear Obstacle Problem with Weighted Variable Exponent
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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.

Author Details

Adil Abbassi

Chakir Allalou

Abderrazak Kassidi

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