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math.AP2026
Good access to the crack and integrability of the full gradient for Griffith almost-minimizers in the plane
Camille Labourie, Lorenzo Lamberti, Antoine Lemenant
We show that, for almost-minimizers of the Griffith energy in the plane, the complement of the crack is locally covered by a finite number of John domains where the displacement sa…
math.AP2025
Finite number of traces for Mumford-Shah minimizers in dimension 2
Camille Labourie, Antoine Lemenant
In this short note, we answer a question raised by E. De Giorgi, showing that a Mumford-Shah minimizer in dimension 2 can only admit three maximum limit values as approaching the s…
math.AP2025
Uniform concentration property for Griffith almost-minimizers
Camille Labourie, Antoine Lememant
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 proper…