A Free Boundary Problem Related to Thermal Insulation
Analysis of PDEs
2016-06-01 v2
Abstract
We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but rather a hypersurface along which a harmonic function satisfies a Robin condition. We show that minimal sets exist, satisfy uniform density estimates, and, under some geometric conditions, have "locally flat" boundaries.
Cite
@article{arxiv.1511.05934,
title = {A Free Boundary Problem Related to Thermal Insulation},
author = {Luis A. Caffarelli and Dennis Kriventsov},
journal= {arXiv preprint arXiv:1511.05934},
year = {2016}
}