Single Layer and Double Layer Potentials

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


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,
$$\left( {Vu} \right)\left( x \right) = \int_\Gamma {E\left( {x - y} \right)} u\left( y \right)d{\Gamma _y} $$
$$\left( {Vu} \right)\left( x \right) = \int\limits_\Gamma {\tfrac{{\partial E\left( {X - Y} \right)}}{{\partial {n_y}}}} u\left( y \right)d{\Gamma _y} $$


Single Layer Fundamental Solution Helmholtz Equation Normal Derivative Jordan Curve 
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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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