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On one phase free boundary problem in $\mathbb{R}^{N}$
- Publication Year :
- 2017
-
Abstract
- We construct a smooth axially symmetric solution to the classical one phase free boundary problem in $\mathbb{R}^{N}$. Its free boundary is of \textquotedblleft catenoid\textquotedblright\ type. This is a higher dimensional analogy of the Hauswirth-Helein-Pacard solution in $\mathbb{R}% ^{2}$ (\cite{Pacard}). The existence of such solution is conjectured in \cite [Remark 2.4]{Pacard}.<br />Comment: 42 pages
- Subjects :
- Mathematics - Analysis of PDEs
Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1705.07345
- Document Type :
- Working Paper