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arXiv · 1304.0699

Anisotropic fractional perimeters

Monika Ludwig
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Abstract

The anisotropic fractional $s$-perimeter with respect to a convex body $K$ in $\rn$ is shown to converge to the anisotropic perimeter with respect to the moment body of $K$ as $s\to 1^-$. A corresponding result is established for anisotropic fractional $s$-seminorms on $BV(\rn)$ (generalizing results of Bourgain, Brezis & Mironescu and D\'avila). The minimizers of the anisotropic fractional $s$-isoperimetric inequality with respect to $K$ are shown to converge to the moment body of $K$. Anisotropic fractional Sobolev inequalities are established.

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Monika Ludwig. 2013-04-02. Anisotropic fractional perimeters. https://doi.org/10.4310/jdg%2F1391192693

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