Advances in Differential Equations

Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov-type operators in non-divergence form

Marco Di Francesco and Sergio Polidoro

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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.

Article information

Source
Adv. Differential Equations Volume 11, Number 11 (2006), 1261-1320.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867597

Mathematical Reviews number (MathSciNet)
MR2277064

Zentralblatt MATH identifier
1153.35312

Subjects
Primary: 35K65: Degenerate parabolic equations
Secondary: 35A08: Fundamental solutions 35K57: Reaction-diffusion equations

Citation

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.


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