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Zeitschrift für Analysis und ihre Anwendungen


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Volume 11, Issue 2, 1992, pp. 173–182
DOI: 10.4171/ZAA/615

Published online: 1992-06-30

Asymptotics of the Solution of a Boundary Integral Equation Under a Small Perturbation of a Corner

Vladimir G. Maz'ya[1] and Ralf Mahnke[2]

(1) Linköping University, Sweden
(2) Universität Rostock, Germany

The boundary integral equation of the Dirichlet problem is considered in a plane domain with a smooth boundary which is a small perturbation of a contour with an angular point. The asymptotics of the solution are given with respect to a perturbation parameter $\epsilon$. The problem studied in this article serves as an example of the use of a general method which is also applicable to the three-dimensional case, to the Neumann problem and to problems of hydrostatics and elasticity.

Keywords: Boundary integral equations, small perturbations

Maz'ya Vladimir, Mahnke Ralf: Asymptotics of the Solution of a Boundary Integral Equation Under a Small Perturbation of a Corner. Z. Anal. Anwend. 11 (1992), 173-182. doi: 10.4171/ZAA/615