For non-smooth compact obstacles, the cut-off resolvent norm of the Laplacian in the Helmholtz scattering problem can grow arbitrarily fast at a sequence of wavenumbers.
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The cut-off resolvent can grow arbitrarily fast in obstacle scattering
For non-smooth compact obstacles, the cut-off resolvent norm of the Laplacian in the Helmholtz scattering problem can grow arbitrarily fast at a sequence of wavenumbers.