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arXiv · 1407.6863

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

S. N. Chandler-Wilde·D. P Hewett
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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)).

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S. N. Chandler-Wilde, D. P Hewett. 2014-07-25. Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens. https://arxiv.org/abs/1407.6863

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