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(\delu(epsilon)\(p-2)delu(epsilon)) = beta(epsilon)(u(epsilon)), (1 < p < infinity) 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. (The case p = 2 has been considered earlier by several authors.).