Sobolev, BV and perimeter extensions in metric measure spaces - Caputo, Emanuele; Koivu, Jesse; Rajala, Tapio (Annales Fennici Mathematici, 2024)
We study extensions of sets and functions in general metric measure spaces. We show that an open set has the strong BV-extension property if and only if it has the strong extension property for sets of finite perimeter. We also prove several implications between the strong BV-extension property and extendability of two different non-equivalent versions of Sobolev \(W^1,1\)-spaces and show via examples that the remaining implications fail.