Mathematical Sciences - Analysis and PDE Seminar - Panu Lahti, (University of Augsburg)

Thursday, March 21, 2019
12:00 pm to 1:00 pm

Location:

Floor/Room #: 
309

Panu Lahti, University of Augsburg
Title: BV functions and Federer's characterization of sets of finite perimeter in metric spaces
Abstract:
We consider the theory of functions of bounded variation (BV functions) in the general setting of a complete metric space equipped with a doubling measure and supporting a Poincaré inequality. Such a theory was first developed by Ambrosio (2002) and Miranda (2003). In particular, I will discuss a metric space proof of Federer's characterization of sets of finite perimeter, i.e. sets whose characteristic functions are BV functions. This characterization states that a set is of finite perimeter if and only if the n-1-dimensional (in metric spaces, codimension one) Hausdorff measure of the set's measure-theoretic boundary is finite.