H\"older regularity for weak solutions of H\"ormander type operators
Analysis of PDEs
2022-12-27 v1
Abstract
Motivated by recent results on the (possibly conditional) regularity for time-dependent hypoelliptic equations, we prove a parabolic version of the Poincar\'e inequality, and as a consequence, we deduce a version of the classical Moser iteration technique using in a crucial way the geometry of the equation. The point of this contribution is to emphasize that one can use the {\sl elliptic} version of the Moser argument at the price of the lack of uniformity, even in the {\sl parabolic } setting. This is nevertheless enough to deduce H\"older regularity of weak solutions. The proof is elementary and unifies in a natural way several results in the literature on Kolmogorov equations, subelliptic ones and some of their variations.
Cite
@article{arxiv.2212.12946,
title = {H\"older regularity for weak solutions of H\"ormander type operators},
author = {G. Citti and M. Mandredini and Y. Sire},
journal= {arXiv preprint arXiv:2212.12946},
year = {2022}
}