Integral Equations and Operator Theory

, Volume 5, Issue 1, pp 562-572

First online:

Integral equations with non integrable kernels

  • J. C. NedelecAffiliated withCentre de Mathématiques Appliquées (ERA/CNRS 747)

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We study here some integral equations linked to the Laplace or the Helmholtz equation, or to the system of elasticity equations. These equations lead to non integrable kernels only defined as finite parts, so that they are quite difficult to approximate. In each case, we introduce a variational formulation which avoids this difficulty and allow us to use stable finite element approximations for these problems