Exact low frequency analysis for a class of exterior boundary value problems for the reduced wave equation in higher dimensions

Abstract

The order of convergence for the low frequency asymptotics of general exterior problems for the Helmholtz equation with variable, possibly nonsmooth coefficients in dimensions greater than two is shown to be ω², the square of the frequency, except of some singular cases. In these cases the asymptotics are characterized completely by some lower order terms in the spherical harmonics expansion of the solution to the static problem.