David Jerison, Ovidiu Savin
Published 2014-10-28Version 1
We show that stable cones for the one-phase free boundary problem are hyperplanes in dimension $4$. As a corollary, both one and two-phase energy minimizing hypersurfaces are smooth in dimension $4$.
Structure of one-phase free boundaries in the plane
Nondegeneracy for stable solutions to the one-phase free boundary problem
Regularity in a one-phase free boundary problem for the fractional Laplacian
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