An isoperimetric inequality related to a Bernoulli problem

Given a bounded domain Ω we look at the minimal parameter Λ(Ω) for which a Bernoulli free boundary value problem for the p -Laplacian has a solution minimising an energy functional. We show that amongst all domains of equal volume Λ(Ω) is minimal for the ball. Moreover, we show that the inequality i...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 39; no. 3-4; pp. 547 - 555
Main Authors Daners, Daniel, Kawohl, Bernd
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.11.2010
Springer Nature B.V
Subjects
Analysis
Calculus of variations
Calculus of Variations and Optimal Control; Optimization
Control
Energy of solution
Free boundaries
Inequalities
Laplace transforms
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Parameter estimation
Partial differential equations
Systems Theory
Theoretical
49R05
35R35
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Summary:Given a bounded domain Ω we look at the minimal parameter Λ(Ω) for which a Bernoulli free boundary value problem for the p -Laplacian has a solution minimising an energy functional. We show that amongst all domains of equal volume Λ(Ω) is minimal for the ball. Moreover, we show that the inequality is sharp with essentially only the ball minimising Λ(Ω). This resolves a problem related to a question asked in Flucher et al. (Reine Angew Math 486:165–204, 1997).
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-010-0324-4