Opuscula Math. 34, no. 1 (2014), 15-28
http://dx.doi.org/10.7494/OpMath.2014.34.1.15

 
Opuscula Mathematica

Existence and uniqueness of the solutions of some degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro

Abstract. In this paper we are interested in the existence of solutions for the Dirichlet problem associated with degenerate nonlinear elliptic equations \[\begin{split}&-\sum_{j=1}^n D_j{\bigl[}{\omega}(x) {\cal A}_j(x, u, {\nabla}u){\bigr]} + b(x, u, {\nabla}u)\,{\omega}(x) + g(x)\,u(x)=\\&= f_0(x) - \sum_{j=1}^nD_jf_j(x) \quad{\rm on}\quad {\Omega}\end{split}\] in the setting of the weighted Sobolev spaces \({\rm W}_0^{1,p}(\Omega, \omega)\).

Keywords: degenerate nonlinear elliptic equations, weighted Sobolev spaces.

Mathematics Subject Classification: 35J70, 35J60.

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Cite this article as:
Albo Carlos Cavalheiro, Existence and uniqueness of the solutions of some degenerate nonlinear elliptic equations, Opuscula Math. 34, no. 1 (2014), 15-28, http://dx.doi.org/10.7494/OpMath.2014.34.1.15

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