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Existence of entropy solutions for degenerate quasilinear elliptic equations in $L^1$
Communications in Mathematics, Tome 22 (2014) no. 1, pp. 57-69 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this article, we prove the existence of entropy solutions for the Dirichlet problem $$ (P)\begin {cases} -\mathrm{div} [{\omega }(x){\cal A} (x,u,{\nabla }u)]=f(x)-\mathrm{div} (G),\text {in }\Omega \\ u(x) = 0,\text {on }{\partial \Omega } \end {cases} $$ where $\Omega $ is a bounded open set of $\real ^N$, $N\geq 2$, $f \in L^1(\Omega )$ and $G/{\omega } \in [L^{p'}(\Omega , \omega )]^N$.
In this article, we prove the existence of entropy solutions for the Dirichlet problem $$ (P)\begin {cases} -\mathrm{div} [{\omega }(x){\cal A} (x,u,{\nabla }u)]=f(x)-\mathrm{div} (G),\text {in }\Omega \\ u(x) = 0,\text {on }{\partial \Omega } \end {cases} $$ where $\Omega $ is a bounded open set of $\real ^N$, $N\geq 2$, $f \in L^1(\Omega )$ and $G/{\omega } \in [L^{p'}(\Omega , \omega )]^N$.
Classification : 35A01, 35J25, 35J60, 35J62, 35J70
Keywords: degenerate elliptic equations; entropy solutions; weighted Sobolev spaces 
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     author = {Cavalheiro, Albo Carlos},
     title = {Existence of entropy solutions for degenerate quasilinear elliptic equations in $L^1$},
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Cavalheiro, Albo Carlos. Existence of entropy solutions for degenerate quasilinear elliptic equations in $L^1$. Communications in Mathematics, Tome 22 (2014) no. 1, pp. 57-69. http://geodesic.mathdoc.fr/item/COMIM_2014_22_1_a4/

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