Higher integrability of the gradient for the Thermal Insulation problem

Camille Labourie; Emmanouil Milakis

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arXiv · 2101.09692

Higher integrability of the gradient for the Thermal Insulation problem

Camille Labourie·Emmanouil Milakis

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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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Camille Labourie, Emmanouil Milakis. 2021-01-24. Higher integrability of the gradient for the Thermal Insulation problem. https://arxiv.org/abs/2101.09692

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