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Mixed Problems of Potential Theory in Spherical Coordinates
Author(s) -
Fabrikant V. I.
Publication year - 1987
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19870671008
Subject(s) - mathematical analysis , elementary function , mathematics , dirichlet distribution , surface (topology) , boundary (topology) , spherical coordinate system , boundary value problem , classical mechanics , physics , geometry
Exact solution in closed form is obtained to the following mixed problem for a charged sphere: an arbitrary charge density distribution is prescribed at the surface of a spherical cap while an arbitrary potential is given at the rest of the sphere. A new method is introduced making the procedure straightforward and elementary, no special functions or integral transforms involved. Some further applications of the method are discussed. A new type of solution is obtained for the Dirichlet problem with discontinuous boundary conditions. Several examples are considered.