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Equilibrium capillary surfaces. (English) Zbl 0583.35002

Grundlehren der Mathematischen Wissenschaften, 284. New York etc.: Springer-Verlag. XV, 245 p. DM 158.00 (1986).
This book is a masterful exposition of capillarity. It is the first, modern, mathematically rigorous treatment of the subject. After an introduction into the theory of capillarity the author presents chapters concerning the symmetric capillary tube, the symmetric sessile drop, the pendent liquid drop, the capillary surfaces without gravity, the capillary contact angle. In chapter 7 he gives existence theorems. A key role is played by a new form of the maximum principle.
The presentation contains specific physical problems and results of experimental corroboration, too. The attention is directed throughout to the unexpected (discontinuous dependence on parameters) and to the results which do not follow readily from the usual perturbation techniques. The book will interest mathematicians and engineers who work in crystal growth from the melt and mathematical biology.
Reviewer: St.Balint

MSC:

35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
86A05 Hydrology, hydrography, oceanography
92B05 General biology and biomathematics