The Transmission Problem on a Three-Dimensional Wedge
Peer reviewed, Journal article
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Date
2019Metadata
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- Institutt for matematiske fag [2530]
- Publikasjoner fra CRIStin - NTNU [38688]
Original version
Archive for Rational Mechanics and Analysis. 2019, 231, 1745–1780. 10.1007/s00205-018-1308-3Abstract
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.