Differential and Integral Equations

On a critical role of Ornstein-Uhlenbeck operators in the Poincaré inequality

Yasuhiro Fujita

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


In this paper, we consider the best constant and its typical lower bound of the Poincaré inequality for diffusion operators on $\mathbb R$. We are interested in the critical case such that these constants are equal. Our goal is to show that they are equal if and only if a diffusion operator is the Ornstein-Uhlenbeck operator with a suitable property. Hence, the Ornstein-Uhlenbeck operator with this property plays a critical role in the Poincaré inequality.

Article information

Differential Integral Equations, Volume 19, Number 12 (2006), 1321-1332.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 35J20: Variational methods for second-order elliptic equations


Fujita, Yasuhiro. On a critical role of Ornstein-Uhlenbeck operators in the Poincaré inequality. Differential Integral Equations 19 (2006), no. 12, 1321--1332. https://projecteuclid.org/euclid.die/1356050291

Export citation