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Regularity of Lipschitz free boundaries in two-phase problems for the p-Laplace operator
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2010 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 225, no 5, 2565-2597 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study the regularity of the free boundary in a general two-phase free boundary problem for the p-Laplace operator and we prove, in particular, that Lipschitz free boundaries are C(1,gamma)-smooth for some gamma is an element of (0, 1). As part of our argument, and which is of independent interest, we establish a Hopf boundary type principle for non-negative p-harmonic functions vanishing on a portion of the boundary of a Lipschitz domain.

Place, publisher, year, edition, pages
Academic Press, 2010. Vol. 225, no 5, 2565-2597 p.
Keyword [en]
p-Harmonic function, Free boundary, Two-phase, Boundary Harnack inequality, Hopf boundary principle, p-Subharmonic, Subsolution, Lipschitz domain, Regularity
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-109561DOI: 10.1016/j.aim.2010.05.005ISI: 000281888400011OAI: oai:DiVA.org:umu-109561DiVA: diva2:859562
Available from: 2015-10-07 Created: 2015-09-30 Last updated: 2017-12-01Bibliographically approved

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