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.
Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov type operators in non-divergence form / M. Di Francesco; S. Polidoro. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 11:11(2006), pp. 1261-1320.
Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov type operators in non-divergence form
DI FRANCESCO, MARCO;POLIDORO, SERGIO
2006
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.