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The Transmission Problem on a Three-Dimensional Wedge

  • Karl-Mikael Perfekt
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Abstract

We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the spectrum. This is carried out in two formulations leading to rather different spectral pictures. One formulation is in terms of square integrable boundary data, the other is in terms of finite energy solutions. We use the layer potential method, which requires the harmonic analysis of a non-commutative non-unimodular group associated with the wedge.

Notes

Acknowledgements

The author thanks Johan Helsing, Anders Karlsson, and Tobias Kuna for helpful discussions. The author is also grateful to the American Institute of Mathematics, San Jose, USA and the Erwin Schrödinger Institute, Vienna, Austria, in each of which some of this work was prepared.

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of ReadingReadingUK

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