Calculus of Variations and Geometric Measure Theory

P. Bouafia - T. De Pauw

A representation formula for members of SBV dual

created by depauw on 29 Oct 2024

[BibTeX]

Published Paper

Inserted: 29 oct 2024

Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
Volume: 25
Number: 1
Pages: 483-493
Year: 2024

ArXiv: 2110.04747 PDF
Links: arxiv

Abstract:

We give an integral representation formula for members of the dual of $SBV(\mathbb{R}^n)$ in terms of functions that are defined on $\widehat{\mathbb{R}^n}$, an appropriate fiber space that we introduce, consisting of pairs $(x,[E]_x)$ where $[E]_x$ is an approximate germ of an $(n-1)$-rectifiable set $E$ at $x$.