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

2014/07/25 by Simon N. Chandler‐Wilde, Chandler-Wilde, S. N., D. P. HEWETT +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #35Q60 #65R20 #Advanced Mathematical Modeling in Engineering #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1407.6863

openalex publication_date 2014/07/25 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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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