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 08 Jan 2018


Submitted Paper

Inserted: 4 jan 2018
Last Updated: 8 jan 2018

Year: 2018

ArXiv: 1801.01300 PDF


In this paper, we extend the result obtained in Juillet, Calc. Var. Partial Differential Equations (2014) for the Heisenberg group to any Carnot group $\mathbb{G}$. Namely, we prove the correspondence between solutions of the sub-elliptic heat equation in $\mathbb{G}$ and gradient flows of the relative entropy functional in the Wasserstein space of probability measures on $\mathbb{G}$.


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