Sobolev and BV spaces on metric measure spaces via derivations and integration by parts

Abstract

We develop a theory of BV and Sobolev Spaces via integration by parts formula in abstract metric spaces; the role of vector fields is played by Weaver's metric derivations. The definition hereby given is shown to be equivalent to many others present in literature.

arXiv admin note: text overlap with arXiv:1111.3730 by other authors