Higher integrability of the gradient for the thermal insulation problem
Camille Labourie
University of Cyprus, Nicosia, CyprusEmmanouil Milakis
University of Cyprus, Nicosia, Cyprus
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Abstract
We prove the higher integrability of the gradient for local 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 .
Cite this article
Camille Labourie, Emmanouil Milakis, Higher integrability of the gradient for the thermal insulation problem. Interfaces Free Bound. 25 (2023), no. 2, pp. 193–216
DOI 10.4171/IFB/481