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On a generalization of the Neumann problem for the Laplace equation outside cuts in a plane
Author(s) -
Krutitskii P. A.,
Chikilev A. O.,
Krutitskaya N. Ch.,
Kolybasova V. V.
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.583
Subject(s) - mathematics , harmonic function , mathematical analysis , laplace transform , jump , fredholm integral equation , directional derivative , laplace's equation , plane (geometry) , fredholm theory , complex plane , infinity , boundary value problem , integral equation , neumann boundary condition , function (biology) , derivative (finance) , geometry , physics , quantum mechanics , evolutionary biology , financial economics , economics , biology
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 © 2004 John Wiley & Sons, Ltd.