Calculus of Variations and Geometric Measure Theory

D. Danielli - A. Petrosyan - H. Shahgholian

A singular perturbation problem for the p-Laplace operator

created on 03 Jun 2002


Accepted Paper

Inserted: 3 jun 2002

Journal: Indiana Univ. Math. Jour.
Year: 2001


In this paper we initiate the study of the nonlinear one phase singular perturbation problem $$ div(
\nabla u\epsilon
{p-2}\nabla u\epsilon)=\beta\epsilon(u\epsilon), \qquad (1<p<\infty) $$ in a domain $\Omega$ of $\R^N$. We prove uniform Lipschitz regularity of uniformly bounded solutions. Once this is done we can pass to the limit to obtain a solution to the stationary case of a combustion problem with a nonlinearity of power type.