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

John Andersson·Norayr Matevosyan·Hayk Mikayelyan
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Abstract

In this paper we consider the following two-phase obstacle-problem-like equation in the unit half-ball $Δu = λ_{+}χ_{\{u>0\}}-λ_{-}χ_{\{u<0\}}, λ_\pm>0$. 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.

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John Andersson, Norayr Matevosyan, Hayk Mikayelyan. 2004-05-28. On the tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem. https://arxiv.org/abs/math/0405562

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