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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.
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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

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References

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