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A singular perturbation problem for the p-Laplace operator
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-1316-7913
2003 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, Vol. 52, no 2, 457-476 p.Article in journal (Refereed) Published
Abstract [en]

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.).

Place, publisher, year, edition, pages
2003. Vol. 52, no 2, 457-476 p.
Keyword [en]
singular perturbation problem, free boundary problem, p-Laplace operator, uniform gradient bounds, free-boundary problem, classical-solutions, regularity, equations, existence
URN: urn:nbn:se:kth:diva-22526ISI: 000183112000008OAI: diva2:341224
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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Shahgholian, Henrik.
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