Optimal regularity and structure of the free boundary for minimizers in\n cohesive zone models

2017/12/21 by Luis Caffarelli, Caffarelli, Luis, Filippo Cagnetti +3 · 1 citation
Computer Science · Engineering · Mathematics · #35B65 #35R35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1712.08133

openalex publication_date 2017/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study optimal regularity and free boundary for minimizers of an energy\nfunctional arising in cohesive zone models for fracture mechanics. Under\nsmoothness assumptions on the boundary conditions and on the fracture energy\ndensity, we show that minimizers are C^{1, 1/2}, and that near non-degenerate\npoints the fracture set is C^{1, \α}, for some \α \∈ (0, 1).\n

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• Gamma convergence for a phase-field cohesive energy

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