Opuscula Math. 33, no. 3 (), 439-453
http://dx.doi.org/10.7494/OpMath.2013.33.3.439
Opuscula Mathematica

# Existence results for Dirichlet problems with degenerated p-Laplacian

Abstract. In this article, we prove the existence of entropy solutions for the Dirichlet problem $(P)\left\{ \begin{array}{ll} & -{\rm div}[{\omega}(x){\vert{\nabla}u\vert}^{p-2}{\nabla}u]= f(x) - {\rm div}(G(x)),\ \ {\rm in} \ \ {\Omega} \\ & u(x)=0, \ \ {\rm in} \ \ {\partial\Omega} \end{array} \right.$ where $$\Omega$$ is a bounded open set of $$\mathbb{R}^N$$ $$(N \geq 2)$$, $$f \in L^1(\Omega)$$ and $$G/\omega \in [L^p(\Omega,\omega)]^N$$.
Keywords: degenerate elliptic equations, entropy solutions, weighted Sobolev spaces.
Mathematics Subject Classification: 35J70, 35J60, 35J92.