Geodesic
Existence and regularity of entropy solutions for strongly nonlinear $p(x)$-elliptic equations
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a100/}
}
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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/