Regularity of flat free boundaries in two-phase problems for the p-Laplace operator

John L. Lewis; Kaj Nyström

doi:10.1016/j.anihpc.2011.09.002

JournalsaihpcVol. 29, No. 1pp. 83–108

Regularity of flat free boundaries in two-phase problems for the p-Laplace operator

John L. Lewis
Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA
- MathSciNet
- zbMATH Open
Kaj Nyström
Department of Mathematics, Umeå University, S-90187 Umeå, Sweden
- MathSciNet
- zbMATH Open

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Abstract

In this paper we continue the study in Lewis and Nyström (2010) [19], concerning the regularity of the free boundary in a general two-phase free boundary problem for the p-Laplace operator, by proving regularity of the free boundary assuming that the free boundary is close to a Lipschitz graph.

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John L. Lewis, Kaj Nyström, Regularity of flat free boundaries in two-phase problems for the p-Laplace operator. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 1, pp. 83–108

DOI 10.1016/J.ANIHPC.2011.09.002