English

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}
}