@Article{Cavalheiro2014,
author = "Cavalheiro, Albo Carlos",
title = "Existence and uniqueness of the solutions of some degenerate nonlinear elliptic equations",
journal = "Opuscula Math.",
year = "2014",
volume = "34",
number = "1",
pages = "15--28",
doi = "http://dx.doi.org/10.7494/OpMath.2014.34.1.15",
url = "http://dx.doi.org/10.7494/OpMath.2014.34.1.15",
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",
issn = "1232-9274"
}