For the half-plane diffraction problem, the Sommerfeld formula is shown to be the limiting amplitude of the unique solution of the associated time-dependent problem in a Sobolev-based functional class.
Optics (Lectures on theoretical physics, Vol
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Time-dependent approach to the uniqueness of the Sommerfeld solution of the diffraction problem by a half-plane
For the half-plane diffraction problem, the Sommerfeld formula is shown to be the limiting amplitude of the unique solution of the associated time-dependent problem in a Sobolev-based functional class.