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Abstract
We consider the Helmholtz singlelayer operator (the trace of the singlelayer potential) as an operator on (Formula presented.) where (Formula presented.) is the boundary of a 3d obstacle. We prove that if (Formula presented.) is (Formula presented.) and has strictly positive curvature then the norm of the singlelayer operator tends to zero as the wavenumber (Formula presented.) 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 combinedfield integral operator for the Helmholtz exterior Dirichlet problem is coercive on such domains in the space (Formula presented.).
Original language  English 

Pages (fromto)  279318 
Journal  BIT Numerical Mathematics 
Volume  55 
Issue number  1 
Early online date  19 Jul 2014 
DOIs  
Publication status  Published  Mar 2015 
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Projects
 1 Finished

Post Doc Fellowship  New Methods and Analysis for Wave Propagation Problems
Engineering and Physical Sciences Research Council
1/04/11 → 31/03/14
Project: Research council