Uniqueness in a Free Boundary Problem - Concepedia

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Uniqueness in a Free Boundary Problem

18

Citations

12

References

2006

Year

John L. Lewis, Andrew Vogel

Communications in Partial Differential Equations

Elliptic EquationRiemann-hilbert ProblemPositive SolutionsFree Boundary ProblemPotential TheoryOverdetermined Boundary ConditionsFunctional AnalysisP LaplacianNonlinear Functional Analysis

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.

References

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On weak reverse hölder inequalities for nondoubling harmonic measures Björn Bennewitz, John L. Lewis Complex Variables Theory and Application An International Journal Integral GeometryMeasure TheoryEngineeringGeneral DomainsQuasiconformal Mapping	2004	24
The one phase free boundary problem for the $p$-Laplacian with non-constant Bernoulli boundary condition Antoine Henrot, Henrik Shahgholian Transactions of the American Mathematical Society	2002	22
Symmetry Theorems and Uniform Rectifiability John L. Lewis, Andrew Vogel Boundary Value Problems Elliptic EquationEngineeringPositive SolutionsRiemann-hilbert ProblemFree Boundary Problem	2006	15

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