On the tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem

2004/05/28 by John Andersson, Norayr Matevosyan, Andersson, John +3 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems #Nonlinear Partial Differential Equations #math.AP #msc:35R35

paper · pdf · doi:10.48550/arxiv.math/0405562

14 pages, 3 figures

arxiv created 2004/05/28 · arxiv updated 2009/12/01

Abstract

In this paper we consider the following two-phase obstacle-problem-like equation in the unit half-ball Δu = λ₊χ_\u>0\-λ_-χ_\u<0\, λ_±>0. We prove that the free boundary touches the fixed one in (uniformly) tangential fashion if the boundary data f and its first and second derivatives vanish at the touch-point.

Citations

• Variational problems with two phases and their free boundaries

Cited by

• Tangential touch between free and fixed boundaries for the fully nonlinear Alt-Phillips problem

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