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

John Andersson, Norayr Matevosyan, and Hayk Mikayelyan

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Submission date: 11. Jun. 2004
Pages: 16
published in: Arkiv för matematik, 44 (2006) 1, p. 1-15 
DOI number (of the published article): 10.1007/s11512-005-0005-2
Bibtex
MSC-Numbers: 35R35
Keywords and phrases: free boundary problems, two-phase obstacle problem, contact points
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Abstract:
In this paper we consider the following two-phase obstacle-problem-like equation in the unit half-ball

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.