Universität Augsburg

Dr. Panu Lahti
Universität Augsburg
spricht am
Donnerstag, 22. November 2018
um
15:00 Uhr
im
Raum 2004 (L1)
über das Thema:
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). I will give an overview of the basic theory and then 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 n1dimensional (in metric spaces, codimension one) Hausdorff measure of the set's measuretheoretic boundary is finite. The proof relies on fine potential theory in the case p=1, much of which seems to be new even in Euclidean spaces. 
Hierzu ergeht herzliche Einladung. 
Prof. Dr. Lisa Beck 