  We study optimal regularity and free boundary for minimizers of an energy
functional arising in cohesive zone models for fracture mechanics. Under
smoothness assumptions on the boundary conditions and on the fracture energy
density, we show that minimizers are $C^{1, 1/2}$, and that near non-degenerate
points the fracture set is $C^{1, \alpha}$, for some $\alpha \in (0, 1)$.
