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.

Calculus and Fine Properties of Functions of Bounded Variation on RCD Spaces

BRENA, Camillo;GIGLI, Nicola
2024

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.
2024
Settore MAT/05 - Analisi Matematica
Bounded variation; Calculus rule; Fine property; RCD space
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/142024
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