Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - M. Scienza

Locality of the perimeter in Carnot groups and chain rule

created by ambrosio on 17 Mar 2009
modified on 31 Mar 2009


Submitted Paper

Inserted: 17 mar 2009
Last Updated: 31 mar 2009

Year: 2009


In the class of Carnot groups we study fine properties of sets of finite perimeter. Improving a recent result by Ambrosio-Kleiner-Le Donne, we show that the perimeter measure is local, i.e. that given any pair of sets of finite perimeter their perimeter measures coincide on the intersection of their essential boundaries. As a consequence we prove a general chain rule for $BV$ functions in this setting.

Keywords: Carnot groups, Sets of finite perimeter, BV functions


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