Search results for "Wulff shape"

showing 2 items of 2 documents

Wulff shape characterizations in overdetermined anisotropic elliptic problems

2017

We study some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and we prove the corresponding Wulff shape characterizations by using some integral identities and just one pointwise inequality. Our techniques provide a somehow unified approach to this variety of problems.

Applied Mathematics010102 general mathematicsDegenerate energy levelsMathematical analysisMathematics::Analysis of PDEsElliptic pdesComputer Science::Numerical Analysis01 natural sciencesMathematics::Numerical Analysis010101 applied mathematicsOverdetermined systemMathematics - Analysis of PDEsNonlinear Sciences::Exactly Solvable and Integrable SystemsSettore MAT/05 - Analisi MatematicaOverdetermined problems. Finsler manifold. Wulff shapes. Torsion problem. CapacityFOS: MathematicsMathematics::Differential GeometryFinsler manifold0101 mathematicsAnisotropyAnalysisAnalysis of PDEs (math.AP)Mathematics
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Some overdetermined problems related to the anisotropic capacity

2018

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.

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)
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