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MiS Preprint
35/2004

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

Abstract

In this paper we consider the following two-phase obstacle-problem-like equation in the unit half-ball \begin{equation*} \Delta u = \lambda_{+}\chi_{\{u>0\}}-\lambda_{-}\chi_{\{u0\}} ,\,\, \lambda_\pm>0. \end{equation*} 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.

Received:
Jun 11, 2004
Published:
Jun 11, 2004
MSC Codes:
35R35
Keywords:
free boundary problems, two-phase obstacle problem, contact points

Related publications

inJournal
2006 Repository Open Access
John Andersson, Norayr Matevosyan and Hayk Mikayelyan

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

In: Arkiv för matematik, 44 (2006) 1, pp. 1-15