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In this paper we prove a $\mathcal C^{1,\alpha}$ regularity result forminimizers of the planar Griffith functional arising from a variational modelof brittle fracture. We prove that any isolated connected component of thecrack, the singular set of a minimizer, is locally a $\mathcal C^{1,\alpha}$curve outside a set of zero Hausdorff measure.

Partial regularity for the crack set minimizing the two-dimensional Griffith energy