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 $\mathbb{R}^d$ ($d=2,3$): 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.

Locations

• SIAM Journal on Mathematical Analysis - View
• arXiv (Cornell University) - View - PDF
• The University of Bath Online Publications Store (The University of Bath) - View - PDF
• Pure (University of Bath) - View - PDF