On the Keldys-Fichera Boundary-value Problem for Degenerate Quasilinear Elliptic Equations

Abstract

We prove existence and uniqueness theorems for the Keldys-Fichera boundary-value problem using pseudo-monotone operators. The equation studied here is quasilinear, elliptic, and its set of degenerate points may be of non-zero measure. We also obtain comparison and maximum principles for this problem.