Inserted: 16 oct 2010
Last Updated: 25 jul 2017
Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci.
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