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 $n - 1$.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.