On one phase free boundary problem in $\mathbb{R}^{N}$
Analysis of PDEs
2017-06-07 v2 Differential Geometry
Abstract
We construct a smooth axially symmetric solution to the classical one phase free boundary problem in . Its free boundary is of \textquotedblleft catenoid\textquotedblright\ type. This is a higher dimensional analogy of the Hauswirth-Helein-Pacard solution in (\cite{Pacard}). The existence of such solution is conjectured in \cite [Remark 2.4]{Pacard}.
Cite
@article{arxiv.1705.07345,
title = {On one phase free boundary problem in $\mathbb{R}^{N}$},
author = {Yong Liu and Kelei Wang and Juncheng Wei},
journal= {arXiv preprint arXiv:1705.07345},
year = {2017}
}
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42 pages