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<p>We resolve a question of Carrapatoso et al. (Arch Ration Mech Anal 243(3):1565–1596, 2022) on Gaussian optimality for the sharp constant in Poincaré-Korn inequalities, under a moment constraint. We also prove stability, showing that measures with a near-optimal constant are quantitatively close to standard Gaussian.</p>

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Stability of the Poincaré–Korn Inequality

  • 期刊论文

  • 发表日期：

    2025年8月19日

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  • Thomas A. Courtade,
  • Max Fathi

摘要

We resolve a question of Carrapatoso et al. (Arch Ration Mech Anal 243(3):1565–1596, 2022) on Gaussian optimality for the sharp constant in Poincaré-Korn inequalities, under a moment constraint. We also prove stability, showing that measures with a near-optimal constant are quantitatively close to standard Gaussian.