  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 linear elasticity with anisotropic, cohesive, or
heterogeneous behavior, minimizers have an essentially closed jump set and are
thus strong minimizers. Our notion of quasiminimality is inspired by and
generalizes previous notions in the literature for the Mumford-Shah functional,
and comprises functions which locally close to the crack have at most a fixed
percentage of excess crack relative to minimizers. As for the case of
minimizers of the Griffith functional, our proof of Ahlfors-regularity relies
on contradiction-compactness and an approximation result for GSBD functions,
showing the robustness of this approach with respect to generalization of bulk
and surface densities.
