Anisotropic isoperimetric inequalities involving boundary momentum, perimeter and volume

We consider a scale invariant functional involving the anisotropic p-momentum, the anisotropic perimeter and the volume. We show that the Wulff shape, associated with the Finsler norm F considered and centered at the origin, is the unique minimizer of the anisotropic functional taken into considerat...

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Bibliographic Details
Published in:Nonlinear analysis 2019-10, Vol.187, p.229-246
Main Authors: Paoli, Gloria, Trani, Leonardo
Format: Article
Language:English
Subjects:
Anisotropic isoperimetric inequality
Anisotropy
Convexity
Inverse anisotropic mean curvature flow
Momentum
Shape derivative
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Summary:We consider a scale invariant functional involving the anisotropic p-momentum, the anisotropic perimeter and the volume. We show that the Wulff shape, associated with the Finsler norm F considered and centered at the origin, is the unique minimizer of the anisotropic functional taken into consideration among all bounded convex sets. •A particular anisotropic and scale invariant functional is considered.•The functional is minimized among all convex and bounded sets.•The Wulff shape is the unique minimizer of this anisotropic functional.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2019.04.017