JournalsjemsVol. 24, No. 7pp. 2443–2492

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

  • Jean-François Babadjian

    Université Paris-Saclay, Orsay, France
  • Flaviana Iurlano

    Sorbonne Université, Paris, France
  • Antoine Lemenant

    Université Paris-Diderot, France
Partial regularity for the crack set minimizing the two-dimensional Griffith energy cover
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Abstract

In this paper we prove a C1,α\mathcal C^{1,\alpha} 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 C1,α\mathcal C^{1,\alpha} 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