Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-12-05T02:11:24.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks concerning a free boundary problem arising in the theory of liquid drops and in plasma physics

Published online by Cambridge University Press:  14 November 2011

John W. Barrett  and
Charles M. Elliott
John W. Barrett
Affiliation:
Department of Mathematics, Imperial College, London SW7 2BZ, U.K.
Charles M. Elliott
Affiliation:
School of Mathematical & Physical Sciences, University of Sussex, Brighton BN1 9QH, U.K.
Get access Rights & Permissions [Opens in a new window]

Synopsis

We consider a generalisation of the liquid drop problem, introduced in [1, Part II], by allowing the upper and lower surfaces to have different surface tension coefficients γv and γu. We study the existence, uniqueness and regularity of this problem. In addition, we show that as γv/γu →0, the solution of this problem converges to the solution of the “plasma problem”.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 1-2 , 1989 , pp. 169 - 181
Copyright
Copyright © Royal Society of Edinburgh 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Benjamin, T. B. and Cocker, A. D.. Liquid drops suspended by soap films. Part I, Part II. Proc. R. Soc. London Ser. A 394 (1984), 19–45.Google Scholar
2Berestycki, H. and Brezis, H.. On a free boundary problem arising in plasma physics. Nonlinear Anal. 4 (1980), 415–436.Google Scholar
3Cocker, A. D., Friedman, A. and McLeod, J. B.. A variational inequality associated with liquid on a soap film. Arch. Rational Mech. Anal. 93 (1986), 15–45.Google Scholar
4Friedman, A.. Variational Principles and Free-Boundary Problems (New York: Wiley, 1982).Google Scholar
5Rodrigues, J.. Obstacle Problems in Mathematical Physics (Amsterdam: North Holland, 1987).Google Scholar
6Temam, R.. A nonlinear eigenvalue problem: the shape at equilibrium of a confined plasma. Arch. Rational Mech. Anal. 60 (1975), 51–73.Google Scholar
7Temam, R.. Remarks on a free boundary problem arising in plasma physics. Comm. Partial Differential Equations 2 (1977), 563–585.CrossRefGoogle Scholar