We prove some Schauder type estimates and an invariant Harnack inequality for a class of degenerate evolution operators of Kolmogorov type. We also prove a Gaussian lower bound for the fundamental solution of the operator and a uniqueness result for the Cauchy problem. The proof of the lower bound is obtained by solving a suitable optimal control problem and using the invariant Harnack inequality.
Titolo: | Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov type operators in non-divergence form |
Autore/i: | DI FRANCESCO, MARCO; POLIDORO, SERGIO |
Autore/i Unibo: | |
Anno: | 2006 |
Rivista: | |
Abstract: | We prove some Schauder type estimates and an invariant Harnack inequality for a class of degenerate evolution operators of Kolmogorov type. We also prove a Gaussian lower bound for the fundamental solution of the operator and a uniqueness result for the Cauchy problem. The proof of the lower bound is obtained by solving a suitable optimal control problem and using the invariant Harnack inequality. |
Data prodotto definitivo in UGOV: | 2006-11-10 |
Appare nelle tipologie: | 1.01 Articolo in rivista |
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