Calculus of Variations and Geometric Measure Theory
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A. Chambolle - V. Crismale

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

created by crismale on 20 Nov 2018

[BibTeX]

preprint

Inserted: 20 nov 2018

Year: 2018

ArXiv: 1811.07147 PDF

Abstract:

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

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