Seminario Dottorato Opening Day 2017/2018 - “Fine properties of functions of bounded variation in Carnot-Caratheodory spaces”

Wednesday 4 October 2017, h. 15:00 - Room 1BC45 - Sebastiano Don

ARGOMENTI: Seminari Dottorato

Our first seminar of 2017/18 will be held as a special event inside the Opening Day of the Doctoral School (15:00, 1BC45)

Wednesday 4 October 2017 h.16:00, Rroom 1BC45
Sebastiano Don (Padova, Dip. Mat.)
“Fine properties of functions of bounded variation in Carnot-Caratheodory spaces”

Functions of bounded variation (BV functions) can be seen as a generalization of Sobolev maps and arise naturally in many problems in Calculus of Variations. Carnot-Caratheodory spaces are particular metric spaces that arise from the study of hypoelliptic differential operators.
In this seminar we will introduce the notions of approximate continuity point, approximate jump point and approximate differentiability point for a generic L^1 function and we will show the so-called fine properties of BV functions, first in the case of Euclidean spaces, and then in the case of Carnot-Caratheodory spaces. In particular, the rectifiability of the approximate jump set, the approximate differentiability almost everywhere and the decomposition formula for the measure derivative of a BV function will be shown.

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