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Existence of entropy solutions for some nonlinear problems in Orlicz spaces. (English) Zbl 1005.35041
Summary: We study in the framework of Orlicz Sobolev spaces $$W_0^1 L_{M}(\Omega)$$ the existence of entropic solutions to the nonlinear elliptic problems $-\text{div} a (x,u,\nabla u)+\text{div} \Phi (u)=f\quad\text{in }\Omega,$ for the case where the second member of the equation $$f\in L^{1} (\Omega)$$, and $$\Phi \in C^0(\mathbb{R}^N)$$.

##### MSC:
 35J60 Nonlinear elliptic equations 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 37A35 Entropy and other invariants, isomorphism, classification in ergodic theory 35A05 General existence and uniqueness theorems (PDE) (MSC2000)
##### Keywords:
growth conditions; $$N$$-function; Sobolev spaces
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