English

Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens

Numerical Analysis 2015-05-22 v2

Abstract

We study the classical first-kind boundary integral equation reformulations of time-harmonic acoustic scattering by planar sound-soft (Dirichlet) and sound-hard (Neumann) screens. We prove continuity and coercivity of the relevant boundary integral operators (the acoustic single-layer and hypersingular operators respectively) in appropriate fractional Sobolev spaces, with wavenumber-explicit bounds on the continuity and coercivity constants. Our analysis is based on spectral representations for the boundary integral operators, and builds on results of Ha-Duong (Jpn J Ind Appl Math 7:489--513 (1990) and Integr Equat Oper Th 15:427--453 (1992)).

Keywords

Cite

@article{arxiv.1407.6863,
  title  = {Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens},
  author = {S. N. Chandler-Wilde and D. P Hewett},
  journal= {arXiv preprint arXiv:1407.6863},
  year   = {2015}
}

Comments

v2 has minor corrections compared to v1. arXiv admin note: substantial text overlap with arXiv:1401.2805