Calculus and fine properties of functions of bounded variation on RCD spaces

Camillo Brena, Nicola Gigli

Published 2022-04-08Version 1

We generalize the classical calculus rules satisfied by functions of bounded variation to the framework of RCD spaces. In the infinite dimensional setting we are able to define an analogue of the distributional differential and on finite dimensional spaces we prove fine properties and suitable calculus rules, such as the Vol'pert chain rule for vector valued functions.