Calculus of Variations and Geometric Measure Theory
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F. Hernandez

Properties of a Hilbertian Norm for Perimeter

created by hernandez on 10 Oct 2017

[BibTeX]

preprint

Inserted: 10 oct 2017

Year: 2017

ArXiv: 1709.08262 PDF

Abstract:

A recent paper of Jerison and Figalli proved a relationship between the $H^{1/2}$ norms of smoothed out indicator functions of sets and their perimeter. We continue this line of investigation and extend it in two ways. First, we describe a description of the situation with general functions of bounded variation, and show that a related quantity controls the size of the jump set. Second, we provide an exact formula in the case of a set of finite perimeter. Several questions remain and are presented here.

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