Integral Representations and Integral Equations
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.
KeywordsIntegral Equation Integral Representation Dirichlet Problem Variational Formulation Helmholtz Equation
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