3 citations · 9 across the 8 of their papers we have counts for
9 papers
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…
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…
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…
Epsilon-regularity for Griffith almost-minimizers in any dimension under a separating condition
Camille Labourie, Antoine Lemenant
In this paper we prove that if (u, K) is an almost-minimizer of the Griffith functional and K is -close to a plane in some ball B R N while separating the ball B in tw…
Regularity improvement for the minimizers of the two-dimensional Griffith energy
Camille Labourie, Antoine Lemenant
In this paper we prove that the singular set of connected minimizers of the planar Griffith functional has Hausdorff dimension strictly less then one, together with the higher inte…
The calibration method for the Thermal Insulation functional
Camille Labourie, Emmanouil Milakis
We provide minimality criteria by construction of calibrations for functionals arising in the theory of Thermal Insulation.
Higher integrability of the gradient for the Thermal Insulation problem
Camille Labourie, Emmanouil Milakis
We prove the higher integrability of the gradient for minimizers of the thermal insulation problem, an analogue of De Giorgi's conjecture for the Mumford-Shah functional. We deduce…
Solutions of the (free boundary) Reifenberg Plateau problem
Camille Labourie
We solve two variants of the Reifenberg problem for all coefficient groups. We carry out the direct method of the calculus of variation and search a solution as a weak limit of a m…
Weak limits of quasiminimizing sequences
Camille Labourie
We show that the weak limit of a quasiminimizing sequence is a quasiminimal set. This generalizes the notion of weak limit of a minimizing sequences introduced by De Lellis, De Phi…