A note on the uniformity of the constant in the Poincaré inequality

2012/08/29 by David Ruiz, Ruiz, David · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1208.6045

openalex publication_date 2012/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classical Poincaré inequality establishes that for any bounded regular domain Ω⊂ \R^N there exists a constant C=C(Ω)>0 such that ∫_Ω |u|² dx ≤ C ∫_Ω |∇ u|² dx ∀ u ∈ H¹(Ω), ∫_Ω u(x) dx=0. In this note we show that C can be taken independently of Ω when Ω is in a certain class of domains. Our result generalizes previous results in this direction.

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