5 citations · 12 across the 19 of their papers we have counts for
5 papers · 1 filter
Fine representation of Hessian of convex functions and Ricci tensor on RCD spaces
Camillo Brena, Nicola Gigli
It is known that on spaces one can define a distributional Ricci tensor . Here we give a fine description of this object by showing that it admits the pol…
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…
Maps of bounded variation from PI spaces to metric spaces
Camillo Brena, Francesco Nobili, Enrico Pasqualetto
We study maps of bounded variation defined on a metric measure space and valued into a metric space. Assuming the source space to satisfy a doubling and Poincaré property, we produ…
Nguyen's approach to Sobolev spaces in metric measure spaces with unique tangents
Camillo Brena, Andrea Pinamonti
We extend Nguyen's characterization of Sobolev spaces to the setting of PI-metric measure spaces such that at a.e. point the tangent space (in the Gromov-Hausdorff sense)…
Functions with bounded Hessian-Schatten variation: density, variational and extremality properties
Luigi Ambrosio, Camillo Brena, Sergio Conti
In this paper we analyze in detail a few questions related to the theory of functions with bounded -Hessian-Schatten total variation, which are relevant in connection with the t…