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

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.

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Bibliographic Details
Published in:Geometric and functional analysis 2015-08, Vol.25 (4), p.1240-1257
Main Authors: Jerison, David, Savin, Ovidiu
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Description
Summary: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.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-015-0335-6