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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the regularity of the Neumann problem for free surfaces with surface tension
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by Walter Craig and Ana-Maria Matei PDF
Proc. Amer. Math. Soc. 135 (2007), 2497-2504 Request permission

Abstract:

In 1952 H. Lewy established that a hydrodynamic free surface which is at least $C^1$ in a neighborhood of a point $q$ situated on the free surface is automatically $C^{\omega }$, possibly in a smaller neighborhood of $q$. This local result is an example which preceeds the theory developed by D. Kinderlehrer, L. Nirenberg and J. Spruck (1977–79), proving that in many cases free surfaces cannot have an arbitrary regularity; in particular, there exist $k,\mu$ such that if the surface in question is $C^{k,\mu }$, then automatically is $C^{\omega }$. In this paper we extend their methods to Neumann type problems for free surfaces with surface tension.
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Additional Information
  • Walter Craig
  • Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
  • Email: craig@math.mcmaster.ca
  • Ana-Maria Matei
  • Affiliation: Department of Mathematics and Computer Science, Loyola University New Orleans, 6363 St. Charles Avenue, New Orleans, Louisiana 70118
  • Email: amatei@loyno.edu
  • Received by editor(s): October 4, 2005
  • Received by editor(s) in revised form: March 20, 2006
  • Published electronically: March 14, 2007
  • Additional Notes: This research was supported in part by the Canada Research Chairs Program and the NSERC through grant # 238452-01.
  • Communicated by: Michael I. Weinstein
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2497-2504
  • MSC (2000): Primary 35J65, 76B15
  • DOI: https://doi.org/10.1090/S0002-9939-07-08776-X
  • MathSciNet review: 2302570