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Keywords:
degenerate elliptic equations; entropy solutions; weighted Sobolev spaces
degenerate elliptic equations; entropy solutions; weighted Sobolev spaces
Summary:
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 $G/{\omega } \in [L^{p'}(\Omega , \omega )]^N$.
References:
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