Sharp High-Frequency Estimates for the Helmholtz Equation and Applications to Boundary Integral Equations

We consider three problems for the Helmholtz equation in interior and exterior domains in $\mathbb{R}^d$ ($d=2,3$): 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.

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