A representation formula for members of SBV dual

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 ${\hat{\mathbb{R}}}^n$, 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 $x$.

7 pages

References in corpus (1)

• Localizable locally determined measurable spaces with negligibles