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MiS Preprint

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

Hayk Mikayelyan and John Andersson


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 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].

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

Related publications

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