(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Elschner, Johannes; Hu, Guanghui
This paper is concerned with the variational approach in weighted
Sobolev spaces to timeharmonic elastic scattering by two-dimensional
unbounded rough surfaces. The rough surface is supposed to be the graph of a
bounded and uniformly Lipschitz continuous function, on which the total
elastic displacement satisfies either the Dirichlet or impedance boundary
condition. We establish uniqueness and existence results for both elastic
plane and point source (spherical) wave incidence, following the recently
developed variational approach in [SIAM J. Math. Anal., 42: 6 (2010), pp.
2554 2580] for the Helmholtz equation. This paper extends our previous
solvability results [SIAM J. Math. Anal., 44: 6 (2012), pp. 4101-4127] in the
standard Sobolev space to the weighted Sobolev spaces.
