Calculus of Variations and Geometric Measure Theory

E. Caputo - J. Koivu - T. Rajala

Sobolev, BV and perimeter extensions in metric measure spaces

created by nobili on 22 Apr 2023
modified by caputo on 14 Mar 2024

[BibTeX]

Published Paper

Inserted: 22 apr 2023
Last Updated: 14 mar 2024

Journal: Annales Fennici Mathematici
Year: 2023
Doi: https://doi.org/10.54330/afm.143899

ArXiv: 2302.10018 PDF

Abstract:

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.