Abstract
We demonstrate that solving the classical problems mentioned in the title on quadrature domains when the given boundary data is rational is as simple as the method of partial fractions. A by-product of our considerations will be a simple proof that the Dirichlet-to-Neumann map on a double quadrature domain sends rational functions on the boundary to rational functions on the boundary. The results extend to more general domains if rational functions are replaced by the class of functions on the boundary that extend meromorphically to the double.
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Research supported by the NSF Analysis and Cyber-enabled Discovery and Innovation programs, grant DMS 1001701.
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Bell, S.R. The Dirichlet and Neumann and Dirichlet-to-Neumann problems in quadrature, double quadrature, and non-quadrature domains. Anal.Math.Phys. 5, 113–135 (2015). https://doi.org/10.1007/s13324-014-0089-6
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DOI: https://doi.org/10.1007/s13324-014-0089-6