On the Best Constant in Poincar´e Inequality over Simple Geometric Domains

CHEN Hong-ru, MA Gao-chao, ZHANG Bei

doi:10.13371/j.cnki.chin.q.j.m.2025.02.003

Chinese Quarterly Journal of Mathematics >

2025 , Vol. 40 >Issue 2: 148 - 157

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.02.003

On the Best Constant in Poincar´e Inequality over Simple Geometric Domains

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School of Mathematics and Statistics, Henan University of Technology, Zhengzhou 450001, China

CHEN Hong-ru (1983-), female, native of Zhengzhou, Henan, associate professor of Henan University of Technology, engages in computational mathematics; MA Gao-chao (1999-), male, native of Zhengzhou, Henan, master of Henan University of Technology, engages in computational mathematics; ZHANG Bei (1990-), female, native of Zhengzhou, Henan, associate professor of Henan University of Technology, engages in computational mathematics.

CHEN Hong-ru (1983-), female, native of Zhengzhou, Henan, associate professor of Henan University of Technology, engages in computational mathematics;

Received date: 2025-01-02

Online published: 2025-06-30

Supported by

Supported by National Natural Science Foundation of China (Grant Nos. 12001170 and 11601124); Innovative Funds Plan of Henan University of Technology (Grant No. 2021ZKCJ11).

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Abstract

In this paper, we explicitly establish Poincar´e inequality for 1≤p <∞ over simple geometric domains, such as segment, rectangle, triangle or tetrahedron. We obtain sharper bounds of the constant in Poincar´e inequality and, in particular, the explicit relation between the constant and the geometric characters of the domain.

Key words： Poincar′e inequality; Poincar′e constant; Bound of constant

Cite this article

CHEN Hong-ru, MA Gao-chao, ZHANG Bei . On the Best Constant in Poincar´e Inequality over Simple Geometric Domains[J]. Chinese Quarterly Journal of Mathematics, 2025 , 40(2) : 148 -157 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.003

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