Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 329-339

A COMPACTNESS RESULT FOR BV FUNCTIONS IN METRIC SPACES

Sebastiano Don and Davide Vittone

Università di Padova, Dipartimento di Matematica
via Trieste 63, 35121 Padova, Italy; sebastiano.don 'at' math.unipd.it

Università di Padova, Dipartimento di Matematica
via Trieste 63, 35121 Padova, Italy; vittone 'at' math.unipd.it

Abstract. We prove a compactness result for bounded sequences (u_j)_j of functions with bounded variation in metric spaces (X,d_j) where the space X is fixed but the metric may vary with j. We also provide an application to Carnot–Carathéodory spaces.

2010 Mathematics Subject Classification: Primary 46E35, 26B30, 26D10, 53C17.

Key words: Functions with bounded variation, metric spaces, compactness theorems, Carnot–Carathéodory spaces.

Reference to this article: S. Don and D. Vittone: A compactness result for BV functions in metric spaces. Ann. Acad. Sci. Fenn. Math. 44 (2019), 329-339.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4415