zbMATH — the first resource for mathematics

Weak differentiability of BV functions on stratified groups. (English) Zbl 1048.49030
Given a simply connected stratified nilpotent Lie group \(\mathbb{G}\) and an open subset \(\Omega\) of \(\mathbb{G}\), the authors introduce a natural concept for functions \(u\in L^1(\Omega)\) to be of bounded variation extending the definition known for the Euclidean case. They then prove the almost everywhere approximate differentiability of these functions and study the size of their approximate discontinuity sets. In further sections they discuss functions of bounded higher order variation and present a weak version of Alexandroff’s differentiability theorem.

49Q15 Geometric measure and integration theory, integral and normal currents in optimization
Full Text: DOI