Communications in Mathematical Physics

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

Corners Always Scatter

  • Eemeli Blåsten
  • Lassi Päivärinta
  • John Sylvester


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.


Open Subset Incident Wave Helmholtz Equation Scattered Wave Harmonic Polynomial 
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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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