Calculus of Variations and Geometric Measure Theory

L. Ambrosio - V. Magnani

Weak differentiability of BV functions on stratified groups

created on 05 Feb 2002
modified on 28 Jan 2004


Published Paper

Inserted: 5 feb 2002
Last Updated: 28 jan 2004

Journal: Math. Z.
Volume: 245
Pages: 123-153
Year: 2003


We prove the almost everywhere approximate differentiability of functions with bounded variation in stratified groups and we study their approximate discontinuity set. We introduce functions of bounded higher order variation and obtain a weak version of Alexandroff differentiability theorem in this context. We present a nontrivial class of functions with second order bounded variation, arising from inf-convolution formula of a suitable ``cost'' function.

Keywords: BV functions, stratified groups, differentiability