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.

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