Existence of strong solutions to the Dirichlet problem for the Griffith energy

作者: Antonin Chambolle , Vito Crismale

DOI: 10.1007/S00526-019-1571-7

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摘要: In this paper we continue the study of Griffith brittle fracture energy minimisation under Dirichlet boundary conditions, suggested by Francfort and Marigo in 1998. a recent paper, proved existence weak minimisers problem. Now show that these are indeed strong solutions, namely their jump set is closed they smooth away from continuous up to boundary. This obtained extending regularity results Conti, Focardi, Iurlano, Chambolle, Iurlano.

参考文章(42)
Nicola Fusco, Irene Fonseca, Regularity results for anisotropic image segmentation models Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze. ,vol. 24, pp. 463- 499 ,(1997)
Diego Pallara, Luigi Ambrosio, Nicola Fusco, Functions of Bounded Variation and Free Discontinuity Problems ,(2000)
William Charles Hector McLean, Strongly Elliptic Systems and Boundary Integral Equations ,(2000)
Charles Bradfield Morrey, Multiple Integrals in the Calculus of Variations ,(1966)
Luigi Ambrosio, Alessandra Coscia, Gianni Dal Maso, Fine Properties of Functions with Bounded Deformation Archive for Rational Mechanics and Analysis. ,vol. 139, pp. 201- 238 ,(1997) , 10.1007/S002050050051
Antonin Chambolle, An approximation result for special functions with bounded deformation Journal de Mathématiques Pures et Appliquées. ,vol. 83, pp. 929- 954 ,(2004) , 10.1016/J.MATPUR.2004.02.004
Antonin Chambolle, A Density Result in Two-Dimensional Linearized Elasticity, and Applications Archive for Rational Mechanics and Analysis. ,vol. 167, pp. 211- 233 ,(2003) , 10.1007/S00205-002-0240-7
G. Bellettini, A. Coscia, G. Dal Maso, Compactness and lower semicontinuity properties in SBD(Omega) Mathematische Zeitschrift. ,vol. 228, pp. 337- 351 ,(1998) , 10.1007/PL00004617