Optimal Regularity and Structure of the Free Boundary for Minimizers in Cohesive Zone Models

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 C1,1/2and that near non-degenerate points the fracture set is C1,alpha for some alpha is an element of(0,1).