552 citations · 2k across the 45 of their papers we have counts for
13 papers · 1 filter
About the general chain rule for functions of bounded variation
Camillo Brena, Nicola Gigli
We give an alternative proof of the general chain rule for functions of bounded variation ([ADM90]), which allows to compute the distributional differential of , where $φ…
Duals and pullbacks of normed modules
Nicola Gigli, Danka Lučić, Enrico Pasqualetto
We give a general description of the dual of the pullback of a normed module. Ours is the natural generalization to the context of modules of the well-known fact that the dual of t…
Local vector measures
Camillo Brena, Nicola Gigli
Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vecto…
Calculus and fine properties of functions of bounded variation on RCD spaces
Camillo Brena, Nicola Gigli
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…
Partial derivatives in the nonsmooth setting
Nicola Gigli, Chiara Rigoni
We study partial derivatives on the product of two metric measure structures, in particular in connection with calculus via modules as proposed by the first named author. Our main…
Korevaar-Schoen's energy on strongly rectifiable spaces
Nicola Gigli, Alexander Tyulenev
We extend Korevaar-Schoen's theory of metric valued Sobolev maps to cover the case of the source space being an RCD space. In this situation it appears that no version of the `subp…