数学季刊 >

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

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

简单几何区域上庞加莱不等式中的最佳常数

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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;

收稿日期: 2025-01-02

  网络出版日期: 2025-06-30

基金资助

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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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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摘要

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.

关键词： Poincar′e inequality; Poincar′e constant; Bound of constant

本文引用格式

陈红如, 马高超, 张蓓 . 简单几何区域上庞加莱不等式中的最佳常数[J]. 数学季刊, 2025 , 40(2) : 148 -157 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.003

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

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