# Structure of one-phase free boundaries in the plane

@article{Jerison2014StructureOO,
title={Structure of one-phase free boundaries in the plane},
author={D. Jerison and Nikola Kamburov},
journal={arXiv: Analysis of PDEs},
year={2014}
}
• Published 2014
• Mathematics
• arXiv: Analysis of PDEs
We study classical solutions to the one-phase free boundary problem in which the free boundary consists of smooth curves and the components of the positive phase are simply-connected. We show that if two components of the free boundary are close, then the solution locally resembles an entire solution discovered by Hauswirth, H\'elein and Pacard, whose free boundary has the shape of a double hairpin. Our results are analogous to theorems of Colding and Minicozzi characterizing embedded minimal… Expand

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