Sobolev, BV and perimeter extensions in metric measure spaces

Kirjoittajat

  • Emanuele Caputo University of Jyväskylä, Department of Mathematics and Statistics
  • Jesse Koivu University of Jyväskylä, Department of Mathematics and Statistics
  • Tapio Rajala University of Jyväskylä, Department of Mathematics and Statistics

Avainsanat:

Sobolev extension, BV-extension, sets of finite perimeter

Abstrakti

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.
Osasto
Articles

Julkaistu

2024-03-12

Viittaaminen

Caputo, E., Koivu, J., & Rajala, T. (2024). Sobolev, BV and perimeter extensions in metric measure spaces. Annales Fennici Mathematici, 49(1), 135–165. https://doi.org/10.54330/afm.143899