Calculus of Variations and Geometric Measure Theory

A. Chambolle - V. Crismale

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

created by crismale on 20 Nov 2018
modified on 13 Dec 2019


Published Paper

Inserted: 20 nov 2018
Last Updated: 13 dec 2019

Journal: Calc. Var. Partial Differential Equations
Volume: 58:136
Year: 2019
Doi: 10.1007/s00526-019-1571-7

ArXiv: 1811.07147 PDF


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.