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Single Layer and Double Layer Potentials

  • Jukka Saranen
  • Gennadi Vainikko
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

For a given boundary value problem in a domain Ω ⊂ ℝ2, one can look for the solution in the form of so called single or double layer potential,
$$\left( {Vu} \right)\left( x \right) = \int_\Gamma {E\left( {x - y} \right)} u\left( y \right)d{\Gamma _y} $$
or
$$\left( {Vu} \right)\left( x \right) = \int\limits_\Gamma {\tfrac{{\partial E\left( {X - Y} \right)}}{{\partial {n_y}}}} u\left( y \right)d{\Gamma _y} $$
.

Keywords

Single Layer Fundamental Solution Helmholtz Equation Normal Derivative Jordan Curve 
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

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jukka Saranen
    • 1
  • Gennadi Vainikko
    • 2
  1. 1.Department of Mathematical SciencesUniversity of OuluOuluFinland
  2. 2.Institute of MathematicsHelsinki University of TechnologyEspooFinland

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