The anisotropic fractional isoperimetric problem with respect to unconditional unit balls

Andreas Kreuml

doi:10.3934/cpaa.2020290

Article Contents

2021, Volume 20, Issue 2: 783-799. Doi: 10.3934/cpaa.2020290

This issue Previous Article Further regularity and uniqueness results for a non-isothermal Cahn-Hilliard equation Next Article The boundedness of multi-linear and multi-parameter pseudo-differential operators

The anisotropic fractional isoperimetric problem with respect to unconditional unit balls

Andreas Kreuml

Technische Universität Wien, Institut für Diskrete Mathematik und Geometrie, Wiedner Hauptstraße 8-10/1046, 1040 Vienna, Austria

Received: April 30, 2020

Revised: September 30, 2020

Early access: December 2020

Published: February 2021

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Abstract

The minimizers of the anisotropic fractional isoperimetric inequality with respect to a convex body $ K $ in $ \mathbb{R}^n $ are shown to be equivalent to star bodies whenever $ K $ is strictly convex and unconditional. From this a Pólya-Szegő principle for anisotropic fractional seminorms is derived by using symmetrization with respect to star bodies.

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Mathematics Subject Classification: Primary:49Q20;Secondary:26D15, 46E35.

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