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 $$C^{1, 1/2}$$ C 1 , 1 / 2 , and that near non-degenerate points the fracture set is $$C^{1, \alpha }$$ C 1 , α , for some $$\alpha \in (0, 1)$$ α ∈ ( 0 , 1 ) .

中文翻译：

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内聚区模型中极小子自由边界的最优规律和结构

我们研究了断裂力学内聚区模型中出现的能量泛函的极小值的最佳规律性和自由边界。在边界条件和裂缝能量密度的平滑假设下，我们表明极小值是 $$C^{1, 1/2}$$ C 1 , 1 / 2 ，并且在非退化点附近，裂缝集是$$C^{1, \alpha }$$ C 1 , α ，对于某些 $$\alpha \in (0, 1)$$ α ∈ ( 0 , 1 ) 。