High-Frequency Estimates on Boundary Integral Operators for the Helmholtz Exterior Neumann Problem

Abstract We study a commonly-used second-kind boundary-integral equation for solving the Helmholtz exterior Neumann problem at high frequency, where, writing $$\Gamma $$ ? boundary of obstacle, relevant integral operators map $$L^2(\Gamma )$$ L 2 ( ) to itself. prove new frequency-explicit bounds on norms both operator and its inverse. The norm are valid piecewise-smooth sharp up factors $$\log k$$ log k (where k is wavenumber), inverse smooth observed be least when with strictly-positive curvature. Together, these results give condition number ; this first time condition-number have been proved obstacles other than balls.