# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.333076

Arkiv for Matematik, 44, (1), 1-15, 2004.6
In this paper we consider the following two-phase obstacle-problem-like equation in the unit half-ball $$\Delta u = \lambda_{+\chi_{\{ u>0 \}}} - \lambda_{-\chi_{\{ u<0 \}}},\quad\lambda_{\pm}>0.$$ We prove that the free boundary touches the fixed boundary (uniformly) tangentially if the boundary data$f$and its first and second derivatives vanish at the touch-point.
@inproceedings{john2004on,
title={On the tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem},
author={John Andersson, Norayr Matevosyan, and Hayk Mikayelyan},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203616563806885},
booktitle={Arkiv for Matematik},
volume={44},
number={1},
pages={1-15},
year={2004},
}

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. 2004. Vol. 44. In Arkiv for Matematik. pp.1-15. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203616563806885.