4 papers
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…
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…
An epsilon-regularity result for Griffith almost-minimizers in the plane
Manuel Friedrich, Camille Labourie, Kerrek Stinson
We present regularity results for the crack set of a minimizer for the Griffith fracture energy, arising in the variational modeling of brittle materials. In the planar setting, we…
Strong existence for free discontinuity problems in linear elasticity
Manuel Friedrich, Camille Labourie, Kerrek Stinson
In this note we show Ahlfors-regularity for a large class of quasiminimizers of the Griffith functional. This allows us to prove that, for a range of free discontinuity problems in…