简单几何区域上庞加莱不等式中的最佳常数

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

数学季刊 ›› 2025, Vol. 40 ›› Issue (2): 148-157.doi: 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

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

收稿日期:2025-01-02 出版日期:2025-06-30 发布日期:2025-06-30
作者简介: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.
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).

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

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

Received:2025-01-02 Online:2025-06-30 Published:2025-06-30
About author: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.
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).

摘要/Abstract

摘要： n 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

Abstract: n 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

中图分类号:

O241.1

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.

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.

简单几何区域上庞加莱不等式中的最佳常数

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

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价