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Poincaré-Steklov integral equations and the Riemann monodromy problem

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Abstract

We consider the Poincaré-Steklov singular integral equation obtained by reducing a boundary value problem for the Laplace operator with a spectral parameter in the boundary condition to the boundary. It is shown that this equation can be restated equivalently in terms of the classical Riemann monodromy problem. Several equations of this type are solved in elliptic functions.

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Authors
  1. A. B. Bogatyrev
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Additional information

Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow Institute of Physical Engineering (Physical-Technical). Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 34, No. 2, pp. 9–22, April–June, 2000.

Translated by V. E. Nazaikinskii

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Bogatyrev, A.B. Poincaré-Steklov integral equations and the Riemann monodromy problem. Funct Anal Its Appl 34, 86–97 (2000). https://doi.org/10.1007/BF02482421

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  • DOI: https://doi.org/10.1007/BF02482421

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