Solvability of nonlinear Dirichlet problem for a class of degenerate elliptic equations

Abstract

We prove an existence result for solution to a class of nonlinear degenerate elliptic equation associated with a class of partial differential operators of the form $Lu\left(x\right)={\sum }_{i,j=1}^n{D}_j\left(a_{ij}\left(x\right)D_{i}u\left(x\right)\right)$, with $D_j=\partial /\partial x_j$, where $a_{ij}:\Omega \to ℝ$ are functions satisfying suitable hypotheses.