Opuscula Math. 33, no. 3 (2013), 439-453

Opuscula Mathematica

Existence results for Dirichlet problems with degenerated p-Laplacian

Albo Carlos Cavalheiro

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.

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  • Albo Carlos Cavalheiro
  • Universidade Estadual de Londrina (State University of Londrina), Departamento de Matemática (Department of Mathematics), 86057-970, Londrina - PR, Brazil
  • Received: 2012-10-29.
  • Accepted: 2012-12-10.
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Cite this article as:
Albo Carlos Cavalheiro, Existence results for Dirichlet problems with degenerated p-Laplacian, Opuscula Math. 33, no. 3 (2013), 439-453, http://dx.doi.org/10.7494/OpMath.2013.33.3.439

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