caa a22 4500 605496773 CHVBK 20210128100538.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10543-014-0506-0 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0506-0 Spence E. Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK aut Bounding acoustic layer potentials via oscillatory integral techniques [Elektronische Daten] [E. Spence] We consider the Helmholtz single-layer operator (the trace of the single-layer potential) as an operator on $$L^2(\Gamma )$$ L 2 ( Γ ) where $$\Gamma $$ Γ is the boundary of a 3-d obstacle. We prove that if $$\Gamma $$ Γ is $$C^2$$ C 2 and has strictly positive curvature then the norm of the single-layer operator tends to zero as the wavenumber $$k$$ k tends to infinity. This result is proved using a combination of (1) techniques for obtaining the asymptotics of oscillatory integrals, and (2) techniques for obtaining the asymptotics of integrals that become singular in the appropriate parameter limit. This paper is the first time such techniques have been applied to bounding norms of layer potentials. The main motivation for proving this result is that it is a component of a proof that the combined-field integral operator for the Helmholtz exterior Dirichlet problem is coercive on such domains in the space $$L^2(\Gamma )$$ L 2 ( Γ ) . Springer Science+Business Media Dordrecht, 2014 Helmholtz equation nationallicence High frequency nationallicence Boundary integral equation nationallicence Layer potential nationallicence Oscillatory integral operator nationallicence BIT Numerical Mathematics Springer Netherlands 55/1(2015-03-01), 279-318 0006-3835 55:1<279 2015 55 10543 https://doi.org/10.1007/s10543-014-0506-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0506-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Spence E. Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/1(2015-03-01), 279-318 0006-3835 55:1<279 2015 55 10543