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Title: Exact solutions to some external mixed problems in potential theory (English)
Author: Fabrikant, Valery I.
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 31
Issue: 3
Year: 1986
Pages: 224-246
Summary lang: English
Summary lang: Russian
Summary lang: Czech
Category: math
Summary: A new and elegant procedure is proposed for the solution of mixed potential problems in a half-space with a circular line of division of boundary conditions. The approach is based on a new type of integral operators with special properties. Two general external problems are solved; i) An arbitrary potential is specified at the boundary outside a circle, and its normal derivative is zero inside; ii) An arbitrary normal derivative is given outside the circle, and be potential is zero inside. Several illustrative examples are considered. Certain methods of application of the proposed technique to the solution of a few complex problems are also discussed. (English)
Keyword: exact solutions
Keyword: mixed problems
Keyword: half-space
Keyword: harmonic function
Keyword: Integral representations
MSC: 31B10
MSC: 31B20
MSC: 35J05
MSC: 35J25
idZBL: Zbl 0625.31004
idMR: MR0837734
DOI: 10.21136/AM.1986.104200
Date available: 2008-05-20T18:30:01Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] I. N. Sneddon: Mixed boundary value problems in potential theory.North-Holland Publishing Company, Amsterdam, 1966. Zbl 0139.28801, MR 0216018
Reference: [2] T. S. Sankar V. I. Fabrikant: Investigations of a two-dimensional integral equation in the theory of elasticity and electrostatics.Journal de Mécanique Théorique et Appliquée, Vol. 2, No. 2, 1983, pp. 285-299. MR 0702239
Reference: [3] I. S. Gradshtein I. M. Ryzhik: Table of Integrals, Series and Products.AP, New York, 1965.
Reference: [4] H. Bateman A. Erdelyi: Higher transcendental functions.Vol. 1, McGraw-Hill, 1953. MR 0058756
Reference: [5] E. W. Hobson: On Green's function for a circular disk, with application to electrostatic problems.Transactions of Cambridge Philosophical Society, Vol. 18, 1900, pp. 277-291.


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