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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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


Export citation

Khayyam Publishing, Inc.

Advances in Differential Equations

New content alerts

Email RSS ToC RSS Article
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more