# Optimal Regularity and Structure of the Free Boundary for Minimizers in Cohesive zone models

created by cagnetti on 21 Dec 2017

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Inserted: 21 dec 2017
Last Updated: 21 dec 2017

Year: 2017

Abstract:

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 $\alpha \in (0, 1)$.