English

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

Functional Analysis 2022-04-11 v1 Metric Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.2204.04174,
  title  = {Calculus and fine properties of functions of bounded variation on RCD spaces},
  author = {Camillo Brena and Nicola Gigli},
  journal= {arXiv preprint arXiv:2204.04174},
  year   = {2022}
}