English

Some remarks on stability of cones for the one-phase free boundary problem

Analysis of PDEs 2014-10-29 v1

Abstract

We show that stable cones for the one-phase free boundary problem are hyperplanes in dimension 44. As a corollary, both one and two-phase energy minimizing hypersurfaces are smooth in dimension 44.

Keywords

Cite

@article{arxiv.1410.7463,
  title  = {Some remarks on stability of cones for the one-phase free boundary problem},
  author = {David Jerison and Ovidiu Savin},
  journal= {arXiv preprint arXiv:1410.7463},
  year   = {2014}
}