2000 character limit reached
On one phase free boundary problem in $\mathbb{R}^{N}$ (1705.07345v2)
Published 20 May 2017 in math.AP and math.DG
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}.
Sponsor
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.