6533b7d9fe1ef96bd126c404

RESEARCH PRODUCT

Some overdetermined problems related to the anisotropic capacity

Chiara BianchiniGiulio CiraoloPaolo Salani

subject

Pure mathematics0211 other engineering and technologiesConvex set02 engineering and technology01 natural sciencesHomothetic transformationOverdetermined systemMathematics - Analysis of PDEs35N25 35B06 35R25FOS: MathematicsConcavity exponent0101 mathematicsAnisotropyMathematics021103 operations researchCapacityApplied Mathematics010102 general mathematicsAnalysiWulff shapeAnisotropic normExponentOverdetermined problemMathematics::Differential GeometryAnalysisAnalysis of PDEs (math.AP)

description

Abstract We characterize the Wulff shape of an anisotropic norm in terms of solutions to overdetermined problems for the Finsler p-capacity of a convex set Ω ⊂ R N , with 1 p N . In particular we show that if the Finsler p-capacitary potential u associated to Ω has two homothetic level sets then Ω is Wulff shape. Moreover, we show that the concavity exponent of u is q = − ( p − 1 ) / ( N − p ) if and only if Ω is Wulff shape.

yearjournalcountryeditionlanguage
2018-03-13
http://arxiv.org/abs/1803.04911