Higher integrability of the gradient for the Thermal Insulation problem

Published 24 Jan 2021 in math.AP | (2101.09692v3)

Abstract: 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 $n-1$.

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