APOct 6, 2015
Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equationsDean Baskin, Euan Spence, Jared Wunsch
We consider three problems for the Helmholtz equation in interior and exterior domains in R^d (d=2,3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for exterior Helmholtz problems.