In this paper we prove a regularity result for minimizers of the planar Griffith functional arising from a variational model of brittle fracture. We prove that any isolated connected component of the crack, the singular set of a minimizer, is locally a curve outside a set of zero Hausdorff measure.
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Jean-François Babadjian, Flaviana Iurlano, Antoine Lemenant, Partial regularity for the crack set minimizing the two-dimensional Griffith energy. J. Eur. Math. Soc. 24 (2022), no. 7, pp. 2443–2492DOI 10.4171/JEMS/1147