2 papers
math.AP2026
Uniform rectifiability of brittle fractures in linear elasticity
Camille Labourie
We prove the uniform rectifiability of brittle fractures in arbitrary dimension. The existing approach for the Mumford-Shah functional, which relies on separation-type properties o…
math.AP2025
Hausdorff dimension of the singular set for Griffith almost-minimizers in the plane
Manuel Friedrich, Camille Labourie, Kerrek Stinson
We consider regularity of the crack set associated to a minimizer of the Griffith fracture energy, often used in modeling brittle materials. We show that the crack is uniformly rec…