Calculus of Variations and Geometric Measure Theory

L. Caffarelli - F. Cagnetti - A. Figalli

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

created by cagnetti on 21 Dec 2017
modified on 04 Mar 2020


Accepted Paper

Inserted: 21 dec 2017
Last Updated: 4 mar 2020

Journal: Arch. Ration. Mech. Anal.
Year: 2020


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