Seminari del Dipartimento di Matematica

Seminario del 2023

Regularity for solutions of sub-Riemannian type operators

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

We prove a parabolic version of the standard Poincaré inequality, and we show that the elliptic version of the Moser argument can be applied even in the parabolic and Kolmogorov setting to deduce the Hölder regularity of the solutions. The price to pay is the lack of uniformity, in the constants. 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. This result is a joint work with M. Manfredini and Y. Sire.