Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - G. Stefani

Heat and entropy flows in Carnot groups

created by stefani on 04 Jan 2018
modified on 29 Oct 2019

[BibTeX]

Submitted Paper

Inserted: 4 jan 2018
Last Updated: 29 oct 2019

Year: 2018

ArXiv: 1801.01300 PDF

Abstract:

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

Keywords: entropy, Gradient Flow, Carnot group, sub-elliptic heat equation


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