### Existence results for degenerate quasilinear elliptic equations in weighted Sobolev spaces

Albo Carlos Cavalheiro
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 17, Number 1 (2010), 141-153.

#### Abstract

In this paper we are interested in the existence of solutions for Dirichlet problem associated to the degenerate quasilinear elliptic equations $$-\,{\rm div}\, [v(x)\,{\cal A}(x, u, {\nabla}u)] + {\omega}(x){\cal A}_0(x,u(x))= f_0 - \sum_{j=1}^nD_jf_j, \ \ {\rm on } \ \ {\Omega}$$ in the setting of the weighted Sobolev spaces ${\rm W}_0^{1,p}(\Omega,\omega,v)$.

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Primary Subjects: 37J70, 35J60