Chinese Quarterly Journal of Mathematics ›› 2025, Vol. 40 ›› Issue (2): 148-157.doi: 10.13371/j.cnki.chin.q.j.m.2025.02.003

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

  

  1. 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).

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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

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