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

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)(1,1)-Poincaré inequality. We prove the equality of 1-modulus and the continuous 1-capacity, extending the known results for 1