In this paper we initiate the study of the nonlinear one phase singular perturbation problem div(|∇uε|p-2∇uε) = βε(uε), (1 < p < ∞) in a domain ω of ℝN. 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).
- Free boundary problem
- P-Laplace operator
- Singular perturbation problem
- Uniform gradient bounds
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