2006 On a critical role of Ornstein-Uhlenbeck operators in the Poincaré inequality
Yasuhiro Fujita
Differential Integral Equations 19(12): 1321-1332 (2006). DOI: 10.57262/die/1356050291

Abstract

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.

Citation

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Yasuhiro Fujita. "On a critical role of Ornstein-Uhlenbeck operators in the Poincaré inequality." Differential Integral Equations 19 (12) 1321 - 1332, 2006. https://doi.org/10.57262/die/1356050291

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35188
MathSciNet: MR2279330
Digital Object Identifier: 10.57262/die/1356050291

Subjects:
Primary: 26D10
Secondary: 35J20

Rights: Copyright © 2006 Khayyam Publishing, Inc.

Vol.19 • No. 12 • 2006
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