Higher integrability of the gradient for the Thermal Insulation problem
Analysis of PDEs
2021-10-05 v3
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 .
Keywords
Cite
@article{arxiv.2101.09692,
title = {Higher integrability of the gradient for the Thermal Insulation problem},
author = {Camille Labourie and Emmanouil Milakis},
journal= {arXiv preprint arXiv:2101.09692},
year = {2021}
}