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Optimal regularity and structure of the free boundary for minimizers in cohesive zone models Cagnetti, Filippo


We consider 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 $C^{1, 1/2}$ on each side of the fracture. Moreover, we prove that near non-degenerate points the fracture set is $C^{1, \alpha}$, for some $\alpha \in (0,1)$. This is joint work with Luis Caffarelli and Alessio Figalli.

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