Elliptic and parabolic quasilinear equations giving rise to a free boundary:the boundary of the support of the solution.

Abstract

This paper gives a very brief review of some properties of solutions of quasilinear scalar elliptic and parabolic partial differential equations in a spatial domain Ω. Emphasis is laid on nonlinearities which allow the support of the solutions to be smaller than Ω. The use of sub- and supersolutions and energy estimates are the only techniques described in any detail, but the paper gives the reader an entree into the vast theoretical literature on these problems. The physical references are selective