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Integral Representations and Integral Equations

  • Jean-Claude Nédélec
Part of the Applied Mathematical Sciences book series (AMS, volume 144)

Abstract

We introduce in this chapter the integral representations of the solutions of the Helmholtz equation. We study the associated integral equations and their main properties. When the wave number k is zero, these integral representations are those associated with the Laplace equation. They have very specific properties. In particular some of the associated integral equations are coercive. We therefore devote special attention to this setting. We will see that they also are the principal parts of the equation associated with the Helmholtz equation.

Keywords

Integral Equation Integral Representation Dirichlet Problem Variational Formulation Helmholtz Equation 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Jean-Claude Nédélec
    • 1
  1. 1.Centre de Mathématiques AppliquéesEcole PolytechniquePalaiseau CedexFrance

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