Onsdag 29 mars 2017, Panu Lahti, MAI
Talare: Panu Lahti, MAI
Titel: Fine boundaries and Federer's characterization of sets of finite perimeter in metric spaces
Tid och plats: Onsdag 29 mars 2017, Hopningspunkten, 13.15–14.15
Sammanfattning: Functions of bounded variation (BV functions) are a class functions that is somewhat more general than Sobolev functions, in that they may have discontinuities and even “jumps”, but are nonetheless differentiable in a very weak sense. Various minimization problems are natural to formulate for the BV class, due to its good compactness properties. In this talk I focus on sets of finite perimeter, which are sets whose characteristic functions are BV functions. In the Euclidean setting, the so-called Federer's characterization states that a set is of finite perimeter if and only if its measure theoretic boundary has finite "surface area". In the more general setting of a metric measure space, the characterization remains an open problem. In the talk I will show how we can obtain a slightly different characterization by replacing the measure theoretic boundary with a new concept, the so-called fine boundary.
Senast uppdaterad: Mon Mar 06 10:20:52 CET 2017