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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
41/2006

On the Non-Tangential Touch Between the Free and Fixed Boundaries for the Two-Phase Obstacle-Like Problem

Hayk Mikayelyan and John Andersson

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_{\{u<0\}} ,\,\, \lambda_\pm>0. \end{equation*} We classify the angles of touch between the free boundary and the fixed one if the boundary data $f$ satisfies certain conditions. This results are connected to the results from [AMM].

Received:
Apr 25, 2006
Published:
Apr 25, 2006
MSC Codes:
35J25, 35J60, 35R35
Keywords:
free boundary problems, boundary regularity, Obstacle Problem

Related publications

inJournal
2012 Repository Open Access
John Andersson and Hayk Mikayelyan

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

In: Mathematische Annalen, 352 (2012) 2, pp. 357-372