0000000000338860

AUTHOR

Chiara Bianchini

showing 4 related works from this author

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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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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An overdetermined problem for the anisotropic capacity

2015

We consider an overdetermined problem for the Finsler Laplacian in the exterior of a convex domain in \({\mathbb {R}}^{N}\), establishing a symmetry result for the anisotropic capacitary potential. Our result extends the one of Reichel (Arch Ration Mech Anal 137(4):381–394, 1997), where the usual Newtonian capacity is considered, giving rise to an overdetermined problem for the standard Laplace equation. Here, we replace the usual Euclidean norm of the gradient with an arbitrary norm H. The resulting symmetry of the solution is that of the so-called Wulff shape (a ball in the dual norm \(H_0\)).

Laplace's equation35A2335B65Applied Mathematics010102 general mathematicsMathematical analysisAnalysi31B15Minkowski inequality01 natural sciences010101 applied mathematicsOverdetermined systemEuclidean distanceMathematics - Analysis of PDEs35J25Norm (mathematics)FOS: Mathematics0101 mathematicsAnisotropyLaplace operatorAnalysisDual normMathematicsAnalysis of PDEs (math.AP)
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A note on an overdetermined problem for the capacitary potential

2016

We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.

Overdetermined boundary value problemCapacityElectrostatic potential010102 general mathematicsMathematical analysisSymmetry in biology·SymmetryComputer Science::Numerical Analysis01 natural sciencesSymmetry (physics)Potential theory010101 applied mathematicsOverdetermined systemMathematics (all)0101 mathematicsMathematics
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