A boundary value problem of mixed type on perforated domains

We analyze a boundary value problem of mixed type with data prescribed on the union of m spheres of small (order m⁻¹) radius. We establish the connection to a particular class of zero-range perturbations of the Laplacian and exploit it for the asymptotic (m→∞) analysis of the solution. It is shown that in the limit problem the “density of scattering length” enters as an effective potential.