Title
Closed BV-extension sets in metric spaces
Abstract
When are BV-extension sets W^{1,1}-extension sets (and vice versa)? In the Euclidean case it was proven by García-Bravo and Rajala that for bounded domains the strong BV-extension property is equivalent to the W^{1,1}-extension property. I will talk about the progression towards the metric case.
I will tie this metric case to another question which goes as follows:
Take a bounded domain, it may be the case that it is not a BV-extension domain, now is it possible to approximate the domain from the inside (or outside) by BV-extension sets (or domains)?
In Euclidean spaces Calderón and Stein (separately) have answered this question rather exhaustively, by showing that Lipschitz domains are W^{1,p}-extension domains.
This talk is based on joint works with Emanuele Caputo, Danka Lučić and Tapio Rajala.
