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

Di Marino Simone

year: 2014
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.

The paper is available on the cvgmt preprint server.