Differential and Integral Equations
- Differential Integral Equations
- Volume 19, Number 12 (2006), 1321-1332.
On a critical role of Ornstein-Uhlenbeck operators in the Poincaré inequality
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.
Differential Integral Equations, Volume 19, Number 12 (2006), 1321-1332.
First available in Project Euclid: 21 December 2012
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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