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

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

2004-05-28

arxiv.org/abs/math/0405562v1

Mathematics

Analysis of PDEs

14 pages, 3 figures

Scientific paper

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

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