Anisotropic isoperimetric inequalities involving boundary momentum, perimeter and volume. (October 2019)

• Record Type: Journal Article
• Authors: Paoli, Gloria; Trani, Leonardo
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 229
• Page End: 246
• Publication Date: 2019-10
• Subjects: 49Q10 -- 47J30; Shape derivative -- Inverse anisotropic mean curvature flow -- Anisotropic isoperimetric inequality; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.04.017
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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. Highlights: 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.