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Reduction of Boundary-Value Problems for the Laplace Equation to Boundary Equations of Calderón—Seeley Type

  • Viktor S. Ryaben’kii
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 30)

Abstract

It will be shown in this chapter how to replace the Laplace equation in a domain by equivalent relations connecting the values of the desired solution \( u|_\Gamma \) and its normal derivative \( \frac{{\partial u}} {{\partial n}}\left| {_\Gamma } \right. \) on the boundary of the domain. These relations, together with the boundary conditions defining the boundary-value problem, form a system of equations for functions defined only on the boundary equivalent to the original boundary-value problem for the Laplace equation in the domain.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Viktor S. Ryaben’kii
    • 1
  1. 1.Keldysh Institute for Applied Mathematics RussianRussian Academy of SciencesMoscowRussia

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