Regularity of Lipschitz free boundaries in two-phase problems for the p-Laplace operator |
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Authors: | John L Lewis Kaj Nyström |
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Institution: | a Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA b Department of Mathematics, Umeå University, S-90187 Umeå, Sweden |
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Abstract: | 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 C1,γ-smooth for some γ∈(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. |
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Keywords: | 35J25 35J70 |
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