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math.AP2021
The Two-Phase Stefan Problem with Anomalous Diffusion
Ioannis Athanasopoulos, Luis Caffarelli, Emmanouil Milakis
The non-local in space two-phase Stefan problem (a prototype in phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admi…
math.AP2021
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.
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…