Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The Helmholtz equation in the exterior of slits in a plane with different impedance boundary conditions on opposite sides of the slits

Author: P. A. Krutitskii
Journal: Quart. Appl. Math. 67 (2009), 73-92
MSC (2000): Primary 35J05, 35J25, 45E05, 76Q05
DOI: https://doi.org/10.1090/S0033-569X-08-01117-4
Published electronically: December 22, 2008
MathSciNet review: 2495072
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Abstract: The boundary value problem for the Helmholtz equation is studied outside slits in a plane. The impedance boundary conditions are specified on the slits. In general, the impedance conditions may be different at different sides of each slit. In a particular case, the impedance conditions may be the same on the sides of each slit. It is proved that the classical solution to the problem exists, and it is unique. The integral representation for a solution to the problem is obtained in the form of potentials, the densities in which are uniquely determined from the uniquely solvable system of the Fredholm integral equations of the second kind and index zero.

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Additional Information

P. A. Krutitskii
Affiliation: KIAM, Department 25, Miusskaya Square 4, Moscow 125047, Russia

DOI: https://doi.org/10.1090/S0033-569X-08-01117-4
Received by editor(s): July 1, 2007
Published electronically: December 22, 2008
Article copyright: © Copyright 2008 Brown University

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