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, which requires no regularity assumptions on the boundary of the screen (other than that the screen is a relatively open bounded subset of the plane), 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; Integr Equ Oper Theory 15:427–453, 1992).
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Chandler-Wilde, S.N., Hewett, D.P. Wavenumber-Explicit Continuity and Coercivity Estimates in Acoustic Scattering by Planar Screens. Integr. Equ. Oper. Theory 82, 423–449 (2015). https://doi.org/10.1007/s00020-015-2233-6
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DOI: https://doi.org/10.1007/s00020-015-2233-6