Advances in Differential Equations
- Adv. Differential Equations
- Volume 11, Number 11 (2006), 1261-1320.
Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov-type operators in non-divergence form
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.
Adv. Differential Equations Volume 11, Number 11 (2006), 1261-1320.
First available in Project Euclid: 18 December 2012
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Di Francesco, Marco; Polidoro, Sergio. Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov-type operators in non-divergence form. Adv. Differential Equations 11 (2006), no. 11, 1261--1320. https://projecteuclid.org/euclid.ade/1355867597.