Partial regularity for the crack set minimizing the two-dimensional Griffith energy
Jean-François Babadjian
Université Paris-Saclay, Orsay, FranceFlaviana Iurlano
Sorbonne Université, Paris, FranceAntoine Lemenant
Université Paris-Diderot, France
Abstract
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.
Cite this article
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. 2443–2492
DOI 10.4171/JEMS/1147