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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.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…