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Differential Equations

, Volume 45, Issue 1, pp 86–101 | Cite as

Boundary value problem for the Laplace equation outside cuts on the plane with different conditions of the third kind on opposite sides of the cuts

  • P. A. Krutitskii
Partial Differential Equations

Abstract

We consider a boundary value problem for the Laplace equation outside cuts on a plane. Boundary conditions of the third kind, which are in general different on different sides of each cut, are posed on the cuts. We show that the classical solution of the problem exists and is unique. We obtain an integral representation for the solution of the problem in the form of potentials whose densities are found from a uniquely solvable system of Fredholm integral equations of the second kind.

Keywords

Operator Mapping Laplace Equation Compact Operator Singular Integral Equation Neumann Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • P. A. Krutitskii
    • 1
  1. 1.Institute for Applied MathematicsRussian Academy of SciencesMoscowRussia

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