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math.FA2023
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…
math.FA2023
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)…
math.FA2023
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…