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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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:
11.06.04
Published:
11.06.04
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