# A singular perturbation problem for the p-Laplace operator

created on 03 Jun 2002

[BibTeX]

Accepted Paper

Inserted: 3 jun 2002

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

Abstract:

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.