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arXiv · 2603.22431

Korn's inequality from the viewpoint of calculus of variations

Gabriele Cassese
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Abstract

We study the best possible constants in Korn-type inequalities and their connection with Morrey's problem in the calculus of variations. We adapt techniques from the analysis of the Beurling-Ahlfors transform to Korn's inequality. In dimension $2$, we obtain a bound that is sharp up to a factor of $1.158$. In general, we show that the constant in Korn's inequality admits a dimension-free bound, and we obtain an estimate that is sharp up to a factor of $\sqrt 3$. We also establish several improvements to estimates in various other function spaces. Using a weighted version of Burkholder's differential subordination theorem, recently introduced in [J. Reine Angew. Math. 824 (2025), pp. 137-166], we also prove a dimension-free weighted version of the inequality for Muckenhoupt weights.

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Gabriele Cassese. 2026-03-23. Korn's inequality from the viewpoint of calculus of variations. https://arxiv.org/abs/2603.22431

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