Volume 54, Issue 4
Anisotropic Elliptic Nonlinear Obstacle Problem with Weighted Variable Exponent

J. Math. Study, 54 (2021), pp. 337-356.

Published online: 2021-06

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• 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.

• Keywords

Entropy solutions, Anisotropic elliptic equations, weighted anisotropic variable exponent Sobolev space.

35J60, 35J87, 35J66

chakir.allalou@yahoo.fr (Chakir Allalou)

abderrazakassidi@gmail.com (Abderrazak Kassidi)

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@Article{JMS-54-337, author = {Adil and Abbassi and abbassi91@yahoo.fr and 16722 and LMACS Laboratory, Mathematics Department, Faculty of Sciences and Techniques, Sultan Moulay Slimane University Beni-Mellal, BP: 523, Morocco and Adil Abbassi and Chakir and Allalou and chakir.allalou@yahoo.fr and 16721 and LMACS Laboratory, Mathematics Department, Faculty of Sciences and Techniques, Sultan Moulay Slimane University Beni-Mellal, BP: 523, Morocco and Chakir Allalou and Abderrazak and Kassidi and abderrazakassidi@gmail.com and 16767 and LMACS Laboratory, Mathematics Department, Faculty of Sciences and Techniques, Sultan Moulay Slimane University Beni-Mellal, BP: 523, Morocco and Abderrazak Kassidi}, title = {Anisotropic Elliptic Nonlinear Obstacle Problem with Weighted Variable Exponent}, journal = {Journal of Mathematical Study}, year = {2021}, volume = {54}, number = {4}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v54n4.21.01}, url = {http://global-sci.org/intro/article_detail/jms/19287.html} }
TY - JOUR T1 - Anisotropic Elliptic Nonlinear Obstacle Problem with Weighted Variable Exponent AU - Abbassi , Adil AU - Allalou , Chakir AU - Kassidi , Abderrazak JO - Journal of Mathematical Study VL - 4 SP - 337 EP - 356 PY - 2021 DA - 2021/06 SN - 54 DO - http://doi.org/10.4208/jms.v54n4.21.01 UR - https://global-sci.org/intro/article_detail/jms/19287.html KW - Entropy solutions, Anisotropic elliptic equations, weighted anisotropic variable exponent Sobolev space. AB -

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.

AdilAbbassi, ChakirAllalou & AbderrazakKassidi. (2021). Anisotropic Elliptic Nonlinear Obstacle Problem with Weighted Variable Exponent. Journal of Mathematical Study. 54 (4). 337-356. doi:10.4208/jms.v54n4.21.01
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