The transmission problem on a three-dimensional wedge
Analysis of PDEs
2018-10-17 v3 Functional Analysis
Spectral Theory
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.
Cite
@article{arxiv.1805.12544,
title = {The transmission problem on a three-dimensional wedge},
author = {Karl-Mikael Perfekt},
journal= {arXiv preprint arXiv:1805.12544},
year = {2018}
}
Comments
35 pages, 1 figure. To appear in Archive for Rational Mechanics and Analysis