Stationarity of the crack-front for the Mumford-Shah problem in 3D

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:462

Article

Lemenant, Antoine¹  Mikayelyan, Hayk² 

[1] Univ Paris 07, LJLL, Paris, France

[2] Univ Nottingham Ningbo, Ningbo, Zhejiang, Peoples R China

关键词: Calculus of variations;    Geometric measure theory;    Mumford-Shah functional;    Stationary solutions;    Cracktip function;   

DOI  :  10.1016/j.jmaa.2018.02.055

来源: Elsevier

【 摘 要 】

In this paper we exhibit a family of stationary solutions of the Mumford-Shah functional in R-3, arbitrary close to a crack-front. Unlike other examples, known in the literature, those are topologically non-minimizing in the sense of Bonnet [4]. We also give a local version in a finite cylinder and prove an energy estimate for minimizers. Numerical illustrations indicate the stationary solutions are unlikely minimizers and show how the dependence on axial variable impacts the geometry of the discontinuity set. A self-contained proof of the stationarity of the cracktip function for the Mumford-Shah problem in 2D is presented. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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