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

John Andersson Institutionen för Matematik, Kungliga Tekniska högskolan Norayr Matevosyan Johann Radon Institut für Angewandte Mathematik, Österreichische Akademie der Wissenschaften Hayk Mikayelyan Mathematisches Institut, Universität Leipzig

TBD mathscidoc: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.
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@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.
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