Revista Matemática Iberoamericana


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Volume 33, Issue 4, 2017, pp. 1369–1396
DOI: 10.4171/RMI/975

Published online: 2017-11-17

Strictly convex corners scatter

Lassi Päivärinta[1], Mikko Salo[2] and Esa V. Vesalainen[3]

(1) Tallinn University of Technology, Estonia
(2) University of Jyväskylä, Finland
(3) Åbo Akademi University, Finland

We prove the absence of non-scattering energies for potentials in the plane having a corner of angle smaller than $\pi$. This extends the earlier result of Blåsten, Päivärinta and Sylvester who considered rectangular corners. In three dimensions, we prove a similar result for any potential with a circular conic corner whose opening angle is outside a countable subset of (0, $\pi$).

Keywords: Corner scattering, non-scattering energies, complex geometrical optics solutions

Päivärinta Lassi, Salo Mikko, Vesalainen Esa: Strictly convex corners scatter. Rev. Mat. Iberoamericana 33 (2017), 1369-1396. doi: 10.4171/RMI/975