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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.
