Uniform concentration property for Griffith almost-minimizers

Abstract

We prove that a Hausdorff limit of Griffith almost-minimizers remains a Griffith almost-minimizer. For this purpose, we introduce a new approach to the uniform concentration property of Dal Maso, Morel and Solimini which does not rely on the coarea formula, non available for symmetric gradient. We then develop several applications, including a general procedure to obtain global minimizers via blow-up limits.

References in corpus (6)

• Existence of strong solutions to the Dirichlet problem for the Griffith energy
• Functionals defined on piecewise rigid functions: Integral representation and $\Gamma$-convergence
• Higher integrability for minimizers of the Mumford-Shah functional
• Epsilon-regularity for Griffith almost-minimizers in any dimension under a separating condition
• Weak limits of quasiminimizing sequences
• Regularity improvement for the minimizers of the two-dimensional Griffith energy