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We consider three problems for the Helmholtz equation in interior andexterior domains in R^d (d=2,3): the exterior Dirichlet-to-Neumann andNeumann-to-Dirichlet problems for outgoing solutions, and the interiorimpedance problem. We derive sharp estimates for solutions to these problemsthat, in combination, give bounds on the inverses of the combined-fieldboundary integral operators for exterior Helmholtz problems.

Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations