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Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations
- Publication Year :
- 2015
-
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.<br />Comment: Version 3: 42 pages; improved exposition in response to referee comments and added several references
- Subjects :
- Mathematics - Analysis of PDEs
Mathematics - Numerical Analysis
35P25, 65N12
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1504.01037
- Document Type :
- Working Paper