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

John Andersson; Norayr Matevosyan; Hayk Mikayelyan

doi:10.1007/s11512-005-0005-2

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

John Andersson, Norayr Matevosyan, Hayk Mikayelyan

Research output: Journal Publication › Article › peer-review

9 Citations (Scopus)

Abstract

In this paper we consider the following two-phase obstacle-problem-like equation in the unit half-ball Δu = λ+χ{u>0}-λ-χ{u<0}, λ± >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.

Original language	English
Pages (from-to)	1-15
Number of pages	15
Journal	Arkiv for Matematik
Volume	44
Issue number	1
DOIs	https://doi.org/10.1007/s11512-005-0005-2
Publication status	Published - Apr 2006
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/s11512-005-0005-2

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abstract = "In this paper we consider the following two-phase obstacle-problem-like equation in the unit half-ball Δu = λ+χ\{u>0\}-λ-χ\{u<0\}, λ± >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.",

author = "John Andersson and Norayr Matevosyan and Hayk Mikayelyan",

note = "Funding Information: Supported by Deutsche Forschungsgemeinschaft and Freistaat Sachsen. The second and third authors thank G{\"o}ran Gustafsson Foundation for visiting appointments to Kungliga Tekniska h{\"o}gskolan, Stockholm.",

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AU - Matevosyan, Norayr

AU - Mikayelyan, Hayk

N1 - Funding Information: Supported by Deutsche Forschungsgemeinschaft and Freistaat Sachsen. The second and third authors thank Göran Gustafsson Foundation for visiting appointments to Kungliga Tekniska högskolan, Stockholm.

PY - 2006/4

Y1 - 2006/4

N2 - In this paper we consider the following two-phase obstacle-problem-like equation in the unit half-ball Δu = λ+χ{u>0}-λ-χ{u<0}, λ± >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.

AB - In this paper we consider the following two-phase obstacle-problem-like equation in the unit half-ball Δu = λ+χ{u>0}-λ-χ{u<0}, λ± >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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DO - 10.1007/s11512-005-0005-2

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

Abstract

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