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

## TL;DR

This paper establishes that in a two-dimensional brittle fracture model, the crack set is mostly smooth and regular, except for a negligible singular part, enhancing understanding of fracture behavior.

## Contribution

It proves a partial regularity result for minimizers of the Griffith energy, showing the crack set is mostly a smooth curve with a negligible singular set.

## Key findings

- Crack set is locally a $ ext{C}^{1,eta}$ curve outside a measure-zero set.
- Singular set of the minimizer has zero Hausdorff measure.
- Provides a rigorous mathematical foundation for crack regularity in brittle fracture models.

## Abstract

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.