A chain rule for a class of evolutive nonlocal hypoelliptic equations
Analysis of PDEs
2019-10-22 v1
Abstract
We prove a chain rule of local type for a class of fractional hypoelliptic equations of Kolmogorov-Fokker-Planck type. We introduce a semigroup based notion of nonlocal \emph{carr\'e du champ} which works successfully in situations in which the infinitesimal generator of the semigroup itself does not necessarily possess a gradient. Our results extend and sharpen the original 2004 chain rule due to A. C\'ordoba and D. C\'ordoba.
Keywords
Cite
@article{arxiv.1910.08803,
title = {A chain rule for a class of evolutive nonlocal hypoelliptic equations},
author = {Federico Buseghin and Nicola Garofalo},
journal= {arXiv preprint arXiv:1910.08803},
year = {2019}
}