*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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