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

Author(s)
Savin, Ovidiu; Jerison, David S
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Abstract
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. Keywords: Free Boundary; Minimal Surface; Free Boundary Problem; Stable Cone; Strict Subsolution
Date issued
2015-07
URI
http://hdl.handle.net/1721.1/115818
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Geometric and Functional Analysis
Publisher
Springer Nature
Citation
Jerison, David and Ovidiu Savin. “Some Remarks on Stability of Cones for the One-Phase Free Boundary Problem.” Geometric and Functional Analysis 25, 4 (July 2015): 1240–1257 © 2015 Springer Basel
Version: Author's final manuscript
ISSN
1016-443X
1420-8970
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