Published Paper

Inserted: 24 nov 2022
Last Updated: 22 jan 2025

Journal: Arch. Ration. Mech. Anal.
Volume: 247
Year: 2023
Doi: 10.1007/s00205-023-01935-z

Abstract:

In this paper we prove that if $(u,K)$ is an almost-minimizer of the Griffith functional and $K$ is epsilon-close to a plane in some ball B in $\mathbb{R}^N$ while separating the ball $B$ in two big parts, then $K$ is $C^{1,\alpha}$ in a slightly smaller ball. Our result contains and generalizes the 2 dimensional result of Babadjian, Iurlano, Lemenant (2022), with a different and more sophisticate approach inspired by Lemenant (2011), using also Labourie (2021) in order to adapt a part of the argument to Griffith minimizers.

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• griffithDimN_V30.pdf