We prove 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; Polidoro, Sergio. - 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

POLIDORO, Sergio
2006

Abstract

We prove 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.
2006
11,11
1261
1320
Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov type operators in non-divergence form / M., DI FRANCESCO; Polidoro, Sergio. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 11,11:(2006), pp. 1261-1320.
M., DI FRANCESCO; Polidoro, Sergio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/612316
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