A singular perturbation problem for the p-Laplace operator

In this paper we initiate the study of the nonlinear one phase singular perturbation problem div(|∇u^ε|^p-2∇u^ε) = β_ε(u^ε), (1 < p < ∞) in a domain ω 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. (The case p = 2 has been considered earlier by several authors).