Geodesic
Existence and regularity of entropy solutions for strongly nonlinear \(p(x)\)-elliptic equations
Electronic journal of differential equations, Tome 2013 (2013)
This article is devoted to study the existence of solutions for the strongly nonlinear $p(x)$-elliptic problem

$\displaylines{ - \operatorname{div} a(x,u,\nabla u) + g(x,u,\nabla u) = f- \operatorname{div} \phi(u) \quad \hbox{in } \Omega, \cr u = 0 \quad \hbox{on } \partial\Omega, }$

with $ f\in L^1(\Omega) $ and $ \phi \in C^{0}(\mathbb{R}^{N})$, also we will give some regularity results for these solutions.
Classification : 35J20, 35J25, 35J60
Keywords: Sobolev spaces with variable exponents, entropy solutions, strongly nonlinear elliptic equations, boundary value problems 
@article{EJDE_2013__2013__a100,
     author = {Azroul,  Elhoussine and Hjiaj,  Hassane and Touzani,  Abdelfattah},
     title = {Existence and regularity of entropy solutions for strongly nonlinear \(p(x)\)-elliptic equations},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1291.35044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a100/}
}
TY  - JOUR
AU  - Azroul,  Elhoussine
AU  - Hjiaj,  Hassane
AU  - Touzani,  Abdelfattah
TI  - Existence and regularity of entropy solutions for strongly nonlinear \(p(x)\)-elliptic equations
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a100/
LA  - en
ID  - EJDE_2013__2013__a100
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%A Touzani,  Abdelfattah
%T Existence and regularity of entropy solutions for strongly nonlinear \(p(x)\)-elliptic equations
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a100/
%G en
%F EJDE_2013__2013__a100
Azroul,  Elhoussine; Hjiaj,  Hassane; Touzani,  Abdelfattah. Existence and regularity of entropy solutions for strongly nonlinear \(p(x)\)-elliptic equations. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a100/