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Exact solutions to some external mixed problems in potential theory
Applications of Mathematics, Tome 31 (1986) no. 3, pp. 224-246
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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.
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.
DOI : 10.21136/AM.1986.104200
Classification : 31B10, 31B20, 35J05, 35J25
Keywords: exact solutions; mixed problems; half-space; harmonic function; Integral representations 
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Fabrikant, Valery I. Exact solutions to some external mixed problems in potential theory. Applications of Mathematics, Tome 31 (1986) no. 3, pp. 224-246. doi: 10.21136/AM.1986.104200

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[3] I. S. Gradshtein I. M. Ryzhik: Table of Integrals, Series and Products. AP, New York, 1965.

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