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On a generalization of the Neumann problem for the Laplace equation outside cuts in a plane

✍ Scribed by P. A. Krutitskii; A. O. Chikilev; N. Ch. Krutitskaya; V. V. Kolybasova

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
144 KB
Volume
28
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

A boundary value problem for harmonic functions outside cuts in a plane is considered. The jump of the normal derivative is specified on the cuts as well as a linear combination of the normal derivative on one side of the cut and the jump of the unknown function. The problem is studied with three different conditions at infinity, which lead to different results on existence and number of solutions. The integral representation for a solution is obtained in the form of potentials density in which satisfies the uniquely solvable Fredholm integral equation of the 2nd kind. Copyright Β© 2004 John Wiley & Sons, Ltd.

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