A singular perturbation problem for the p-Laplace operator

D. Danielli, A. Petrosyan, H. Shahgholian

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

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).

Original languageEnglish (US)
Pages (from-to)457-476
Number of pages20
JournalIndiana University Mathematics Journal
Volume52
Issue number2
DOIs
StatePublished - 2003
Externally publishedYes

Keywords

  • Free boundary problem
  • P-Laplace operator
  • Singular perturbation problem
  • Uniform gradient bounds

ASJC Scopus subject areas

  • Mathematics(all)

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