Calculus of Variations and Geometric Measure Theory

D. Vittone

Lipschitz surfaces, perimeter and trace theorems for BV functions in Carnot-Carathèodory spaces

created by vittone on 16 Oct 2010
modified on 25 Jul 2017


Published Paper

Inserted: 16 oct 2010
Last Updated: 25 jul 2017

Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci.
Volume: XI
Number: 4
Pages: 939--998
Year: 2012
Doi: 10.2422/2036-2145.201010_007


We introduce intrinsic Lipschitz hypersurfaces in Carnot-Carathéodory spaces and prove that intrinsic Lipschitz domains have locally finite perimeter. We also show the existence of a boundary trace operator for functions with bounded variation on Lipschitz domains and obtain extension results for such functions. In particular, we characterize their trace space.

Keywords: Carnot-Carathéodory spaces, Traces, perimeter, bounded variation