Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2023

Epsilon-regularity for Griffith almost-minimizers in any dimension under a separating condition

Résumé

In this paper we prove that if $(u, K)$ is an almost-minimizer of the Griffith functional and K is $\varepsilon$-close to a plane in some ball $B \subset \mathbf{R}^N$ 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 [4], with a different and more sophisticate approach inspired by [23, 24], using also [20] in order to adapt a part of the argument to Griffith minimizers.

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Dates et versions

hal-03870066 , version 1 (24-11-2022)
hal-03870066 , version 2 (14-11-2023)

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Camille Labourie, Antoine Lemenant. Epsilon-regularity for Griffith almost-minimizers in any dimension under a separating condition. Archive for Rational Mechanics and Analysis, 2023, 247, pp.105. ⟨10.1007/s00205-023-01935-z⟩. ⟨hal-03870066v2⟩
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