Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Lemniscate growth

Lemniscate growth It was recently noticed that lemniscates do not survive Laplacian growth (Khavinson et al. in Math Res Lett 17:335–341, 2010). This raises the question: “Is there a growth process for which polynomial lemniscates are solutions?” The answer is “yes”, and the law governing the boundary velocity is reciprocal to that of Laplacian growth. Viewing lemniscates as solutions to a moving-boundary problem gives a new perspective on results from classical potential theory, and interesting properties emerge while comparing lemniscate growth to Laplacian growth. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Loading next page...
 
/lp/springer-journals/lemniscate-growth-p1gFSjZkIe
Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Basel
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-012-0038-1
Publisher site
See Article on Publisher Site

Abstract

It was recently noticed that lemniscates do not survive Laplacian growth (Khavinson et al. in Math Res Lett 17:335–341, 2010). This raises the question: “Is there a growth process for which polynomial lemniscates are solutions?” The answer is “yes”, and the law governing the boundary velocity is reciprocal to that of Laplacian growth. Viewing lemniscates as solutions to a moving-boundary problem gives a new perspective on results from classical potential theory, and interesting properties emerge while comparing lemniscate growth to Laplacian growth.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Sep 30, 2012

References