Affiliation:
1. Academy of Mathematics and Systems Science , Chinese Academy of Sciences , Beijing 100190 , P. R. China
Abstract
Abstract
Bonicatto, Pasqualetto and Rajala (2020) proved that a decomposition theorem for sets of finite perimeter
into indecomposable sets, known to hold in Euclidean spaces, holds also in complete metric spaces equipped with
a doubling measure, supporting a Poincaré inequality, and satisfying an isotropicity
condition. We show that the last assumption can be removed.
Subject
Applied Mathematics,Analysis
Reference13 articles.
1. L. Ambrosio,
Fine properties of sets of finite perimeter in doubling metric measure spaces,
Set-Valued Var. Anal. 10 (2002), no. 2–3, 111–128.
2. L. Ambrosio, V. Caselles, S. Masnou and J.-M. Morel,
Connected components of sets of finite perimeter and applications to image processing,
J. Eur. Math. Soc. (JEMS) 3 (2001), no. 1, 39–92.
3. L. Ambrosio, N. Fusco and D. Pallara,
Functions of Bounded Variation and Free Discontinuity Problems,
Oxford Math. Monogr.,
The Clarendon, New York, 2000.
4. L. Ambrosio, M. Miranda, Jr. and D. Pallara,
Special functions of bounded variation in doubling metric measure spaces,
Calculus of Variations: Topics From the Mathematical Heritage of E. De Giorgi,
Quad. Mat. 14,
Seconda Università degli Studi di Napoli, Caserta (2004), 1–45.
5. A. Björn and J. Björn,
Nonlinear Potential Theory on Metric Spaces,
EMS Tracts Math 17,
European Mathematical Society, Zürich, 2011.