Wavenumber-explicit continuity and coerciv- ity estimates in acoustic scattering by planar screens
نویسندگان
چکیده
We study the classical first-kind boundary integral equation reformulations of time-harmonic acoustic scattering by planar soundsoft (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) and Integr Equat Oper Th 15:427–453 (1992)). Mathematics Subject Classification (2010). 65R20, 35Q60.
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