REGULARITY FOR THE INTERFACES OF EVOLUTIONARY P-LAPLACIAN FUNCTIONS

Abstract

The support of an evolutionary p-Laplacian function has a finite propagation speed. Here we consider various questions involving the interface, which is the boundary of the open set where the solution is positive. We especially study the initial behaviour and regularity of the interface. We find a necessary and sufficient condition for the interface to move. For the regularity questions we show that the interface is globally Holder continuous employing the Harnack principle. Furthermore, we prove that the interface is Lipschitz, continuous after a large time and globally Lipschitz continuous if the initial data satisfy certain nondegeneracy conditions.