3 papers
math.MG2025
Closed BV-extension and -extension sets
Emanuele Caputo, Jesse Koivu, Danka Lučić +1
This paper studies the relations between extendability of different classes of Sobolev and functions from closed sets in general metric measure spaces. Under the ass…
math.MG2023
Approximation by BV-extension sets via perimeter minimization in metric spaces
Jesse Koivu, Danka Lučić, Tapio Rajala
We show that every bounded domain in a metric measure space can be approximated in measure from inside by closed -extension sets. The extension sets are obtained by minimizing…
math.MG2023
Sobolev, BV and perimeter extensions in metric measure spaces
Emanuele Caputo, Jesse Koivu, Tapio Rajala
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…