Sharp High-Frequency Estimates for the Helmholtz Equation and Applications to Boundary Integral Equations Academic Article uri icon

abstract

  • © 2016 Society for Industrial and Applied Mathematics. We consider three problems for the Helmholtz equation in interior and exterior domains in ℝd (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.

author list (cited authors)

  • Baskin, D., Spence, E. A., & Wunsch, J.

citation count

  • 23

publication date

  • January 2016