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

• Main Author: Albo Carlos Cavalheiro
• Format: Article
• Language: English
• Published: AGH Univeristy of Science and Technology Press 2014-01-01
• Series: Opuscula Mathematica
• Subjects: degenerate nonlinear elliptic equations; weighted Sobolev spaces
• Online Access: http://www.opuscula.agh.edu.pl/vol34/1/art/opuscula_math_3402.pdf

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 \({\rm W}_0^{1,p}(\Omega, \omega)\).