Calculus of Variations and Geometric Measure Theory

J. F. Babadjian - F. Iurlano - A. Lemenant

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

created by lemenant on 22 May 2019
modified by iurlano on 04 Jan 2022


Accepted Paper

Inserted: 22 may 2019
Last Updated: 4 jan 2022

Journal: J. Eur. Math. Soc.
Year: 2019


In this paper we prove a $\mathcal C^{1,\alpha}$ 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 $\mathcal C^{1,\alpha}$ curve outside a set of zero Hausdorff measure.