We prove the correspondence between the solutions of the sub-elliptic heat equation in a Carnot group G and the gradient flows of the relative entropy functional in the Wasserstein space of probability measures on G. Our result completely answers a question left open in a previous paper by N. Juillet, where the same correspondence was proved for G = Hn, the n-dimensional Heisenberg group.

Heat and entropy flows in Carnot groups

Ambrosio L.
;
Stefani G.
2020

Abstract

We prove the correspondence between the solutions of the sub-elliptic heat equation in a Carnot group G and the gradient flows of the relative entropy functional in the Wasserstein space of probability measures on G. Our result completely answers a question left open in a previous paper by N. Juillet, where the same correspondence was proved for G = Hn, the n-dimensional Heisenberg group.
2020
Settore MAT/05 - Analisi Matematica
Carnot group; Entropy; Gradient flow; Sub-elliptic heat equation;
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/101235
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