Stability of the Poincar\'e-Korn inequality
Thomas A. Courtade, Max Fathi
TL;DR
This paper proves the Gaussian measure's optimality for the Poincaré-Korn inequality's sharp constant and establishes stability results, demonstrating measures close to optimal are quantitatively near Gaussian.
Contribution
It resolves a question on Gaussian optimality and provides quantitative stability results for measures near the optimal constant in the Poincaré-Korn inequality.
Findings
Gaussian measure is optimal for the Poincaré-Korn inequality.
Measures with near-optimal constants are quantitatively close to Gaussian.
The results confirm stability of the inequality under perturbations.
Abstract
We resolve a question of Carrapatoso et al. on Gaussian optimality for the sharp constant in Poincar\'e-Korn inequalities, under a moment constraint. We also prove stability, showing that measures with near-optimal constant are quantitatively close to standard Gaussian.
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Taxonomy
TopicsPoint processes and geometric inequalities · Mathematical functions and polynomials · Advanced Differential Equations and Dynamical Systems