English

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 n1n-1.

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}
}
R2 v1 2026-06-23T22:27:53.136Z