Lipschitz surfaces, perimeter and trace theorems for BV functions in Carnot-Carathéodory spaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 4, p. 939-998

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.

Published online : 2018-06-21
Classification:  53C17,  46E35
@article{ASNSP_2012_5_11_4_939_0,
     author = {Vittone, Davide},
     title = {Lipschitz surfaces, perimeter and trace theorems for BV functions in Carnot-Carath\'eodory spaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 11},
     number = {4},
     year = {2012},
     pages = {939-998},
     zbl = {1270.53068},
     mrnumber = {3060706},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2012_5_11_4_939_0}
}
Vittone, Davide. Lipschitz surfaces, perimeter and trace theorems for BV functions in Carnot-Carathéodory spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 4, pp. 939-998. http://www.numdam.org/item/ASNSP_2012_5_11_4_939_0/

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