Remarks concerning a free boundary problem arising in the theory of liquid drops and in plasma physics. (English) Zbl 0668.76137

We consider a generalisation of the liquid drop problem, introduced by T. B. Benjamin and A. D. Cocker [Proc. R. Soc. Lond., Ser. A 394, 33-45 (1984; Zbl 0573.76091); ibid. 19-32 (1984; Zbl 0573.76090)] by allowing the upper and lower surfaces to have different surface tension coefficients \(\gamma_ v\) and \(\gamma_ u\). We study the existence, uniqueness and regularity of this problem. In addition, we show that as \(\gamma_ v/\gamma_ u\to 0\), the solution of this problem converges to the solution of the “plasma problem”.


76T99 Multiphase and multicomponent flows
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
49S05 Variational principles of physics
Full Text: DOI


[1] DOI: 10.1080/03605307708820039 · Zbl 0355.35023 · doi:10.1080/03605307708820039
[2] DOI: 10.1007/BF00281469 · Zbl 0328.35069 · doi:10.1007/BF00281469
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[4] DOI: 10.1098/rspa.1984.0067 · Zbl 0573.76090 · doi:10.1098/rspa.1984.0067
[5] DOI: 10.1007/BF00250843 · doi:10.1007/BF00250843
[6] DOI: 10.1016/0362-546X(80)90083-8 · Zbl 0437.35032 · doi:10.1016/0362-546X(80)90083-8
[7] Friedman, Variational Principles and Free-Boundary Problems (1982)
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