3 papers
math.AP2021
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…
math.CA2020
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…
math.CA2020
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…