Geodesic
Sobolev, BV and perimeter extensions in metric measure spaces
Emanuele Caputo1 ; Jesse Koivu1 ; Tapio Rajala1
1University of Jyväskylä, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 135–165

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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.
DOI : 10.54330/afm.143899
Keywords: Sobolev extension, BV-extension, sets of finite perimeter

Emanuele Caputo  1   ; Jesse Koivu  1   ; Tapio Rajala  1

1 University of Jyväskylä, Department of Mathematics and Statistics 
Emanuele Caputo; Jesse Koivu; Tapio Rajala. Sobolev, BV and perimeter extensions in metric measure spaces. Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 135–165. doi: 10.54330/afm.143899
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