| Abstract: | We investigate the problem of the free surface of a drop in a force field. Under the assumption of a certain symmetry and smallness of the force field, this problem reduces to an equation with a contraction operator from which there follows the existence and uniqueness of a nearly spherical solution.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 52, pp. 160–174, 1975.In conclusion, the author expresses his deep gratitude to N. N. Ural'tseva for suggesting the problem and for a series of critical remarks as well as to O. A. Ladyzhenskaya for her interest in the paper. |
