A priori bound for elastic scattering of incident plane waves from a diffraction grating

This paper investigates elastic scattering by a grating with plane incident waves, where the grating profile is assumed to be the graph of a periodic Lipschitz continuous function. Based on Rellich identities, an a priori bound is established, which is explicitly dependent on the angular frequency, the truncated height and the Lipschitz constant of the grating profile. Moreover, a similar explicit bound can be extended to a more general case with random periodic structures.