Weak differentiability of BV functions on stratified groups
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.
functions of bounded higher order variation
scientific article; zbMATH DE number 2018248