Corners Always Scatter

We study time harmonic scattering for the Helmholtz equation in $${\mathbb{R}^n}$$Rn. 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.

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