Higher integrability of the gradient for the Thermal Insulation problem

Camille Labourie (1) , Emmanouil Milakis (1)

1 UCY - University of Cyprus [Nicosia]

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 that the singular part of the free boundary has Hausdorff dimension strictly less than $n-1$.

Mots clés: free boundary; thermal insulation; higher integrability

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Camille Labourie, Emmanouil Milakis. Higher integrability of the gradient for the Thermal Insulation problem. 2021. ⟨hal-03207514v2⟩