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Communications in Mathematical Physics

, Volume 331, Issue 2, pp 725–753 | Cite as

Corners Always Scatter

  • Eemeli Blåsten
  • Lassi Päivärinta
  • John Sylvester
Article

Abstract

We study time harmonic scattering for the Helmholtz equation in \({\mathbb{R}^n}\). We show that certain penetrable scatterers with rectangular corners scatter every incident wave nontrivially. Even though these scatterers have interior transmission eigenvalues, the relative scattering (a.k.a. far field) operator has a trivial kernel and cokernel at every real wavenumber.

Keywords

Open Subset Incident Wave Helmholtz Equation Scattered Wave Harmonic Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Eemeli Blåsten
    • 1
  • Lassi Päivärinta
    • 1
  • John Sylvester
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  2. 2.Department of MathematicsUniversity of WashingtonSeattleUSA

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