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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