Properties of a Hilbertian Norm for Perimeter

2017/09/24 by Felipe Hernández, Felipe Hernandez, Hernandez, Felipe
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Point processes and geometric inequalities #Statistical and numerical algorithms #math.FA

paper · pdf · doi:10.48550/arxiv.1709.08262

openalex publication_date 2017/09/24 · arxiv created 2017/10/10 · arxiv updated 2017/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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