Electronic Journal of Differential Equations (Oct 2002)
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. Submitted April 27, 2002. Published October 10, 2002. Math Subject Classifications: 35J65, 35J30. Key Words: Keldys-Fichera; existence; uniqueness; maximum principle; comparison principle.