A comparison principle for quasilinear elliptic equations and its application

Zhiren Jin and Kirk Lancaster

Vol. 184 (1998), No. 2, 279–294

DOI: 10.2140/pjm.1998.184.279

Abstract

A comparison principle for a class of quasilinear elliptic equations is proved. An application of the comparison principle is given to prove the uniqueness of solutions of Dirichlet problems for a class of elliptic equations with jump discontinuous boundary data. The comparison principle is improved from the one given by Serrin. The uniqueness is proved by reducing the equation to an associated elliptic equation by viewing the graph of the solution from the side.

Milestones

Received: 22 November 1996

Published: 1 June 1998