TY  - JOUR
ID  - Cavalheiro2013
LB  - Cavalheiro2013
AU  - Cavalheiro, Albo Carlos
TI  - Existence results for Dirichlet problems with degenerated p-Laplacian
ST  - Existence results for Dirichlet problems with degenerated p-Laplacian
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2013
VL  - 33
IS  - 3
SP  - 439
EP  - 453
DO  - http://dx.doi.org/10.7494/OpMath.2013.33.3.439
UR  - http://dx.doi.org/10.7494/OpMath.2013.33.3.439
AB  - 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 \(G/\omega \in [L^p(\Omega,\omega)]^N\).
KW  - degenerate elliptic equations
KW  - entropy solutions
KW  - weighted Sobolev spaces
SN  - 1232-9274
ER  -