Uniqueness in a free boundary problem

John L. Lewis; Andrew L. Vogel

doi:10.1080/03605300500455909

Uniqueness in a free boundary problem

John L. Lewis, Andrew L. Vogel

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We study overdetermined boundary conditions for positive solutions to the p Laplacian in a bounded domain D. We show these conditions imply uniqueness in certain free boundary problems.

Original language	English (US)
Pages (from-to)	1591-1614
Number of pages	24
Journal	Communications in Partial Differential Equations
Volume	31
Issue number	11
DOIs	https://doi.org/10.1080/03605300500455909
State	Published - Nov 1 2006

Keywords

Elliptic
Green's function
Hausdorff measure
Overdetermined
Symmetry
p Laplacian

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605300500455909

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title = "Uniqueness in a free boundary problem",

abstract = "We study overdetermined boundary conditions for positive solutions to the p Laplacian in a bounded domain D. We show these conditions imply uniqueness in certain free boundary problems.",

keywords = "Elliptic, Green's function, Hausdorff measure, Overdetermined, Symmetry, p Laplacian",

author = "Lewis, {John L.} and Vogel, {Andrew L.}",

note = "Funding Information: Lewis was partially supported by NSF grant 0139748.",

year = "2006",

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doi = "10.1080/03605300500455909",

language = "English (US)",

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journal = "Communications in Partial Differential Equations",

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AU - Lewis, John L.

AU - Vogel, Andrew L.

N1 - Funding Information: Lewis was partially supported by NSF grant 0139748.

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Y1 - 2006/11/1

N2 - We study overdetermined boundary conditions for positive solutions to the p Laplacian in a bounded domain D. We show these conditions imply uniqueness in certain free boundary problems.

AB - We study overdetermined boundary conditions for positive solutions to the p Laplacian in a bounded domain D. We show these conditions imply uniqueness in certain free boundary problems.

KW - Elliptic

KW - Green's function

KW - Hausdorff measure

KW - Overdetermined

KW - Symmetry

KW - p Laplacian

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EP - 1614

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 11

ER -

Uniqueness in a free boundary problem

Abstract

Keywords

ASJC Scopus subject areas

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