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

Abstract

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.

Version 3: 42 pages; improved exposition in response to referee comments and added several references

References in corpus (2)

• Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering
• Sharp norm estimates of layer potentials and operators at high frequency

Cited by in corpus (1)

• A first order system least squares method for the Helmholtz equation