Comparisons of relative BV-capacities and Sobolev capacity in metric spaces

✍ Scribed by Heikki Hakkarainen; Nageswari Shanmugalingam

• Book ID: 103849088
• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 317 KB
• Volume: 74
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2011.05.036

✦ Synopsis

We study relations between the variational Sobolev 1-capacity and versions of variational BV-capacity in a complete metric space equipped with a doubling measure and supporting a weak (1, 1)-Poincaré inequality. We prove the equality of 1-modulus and the continuous 1-capacity, extending the known results for 1 < p < ∞ to also cover the more geometric case p = 1. Then we give alternative definitions for variational BV-capacities and obtain equivalence results between them. Finally we study relations between total 1-capacity and versions of BV-capacity.