A boundary value problem of mixed type on perforated domains

Article type: Research Article

Authors: Figari, R.^; | Teta, A.

Affiliations: Dipartimento di Scienze Fisiche, Mostra d'Oltremare-Pad. 19, 80125 Napoli, Italy | Institut für Mathematik, Ruhr-Universität Bochum, W-4630 Bochum 1, Germany

Note: [] Correspondence to: R. Figari, Dipartimento di Scienze Fisiche, Mostra d'Oltremare-Pad. 19, 80125 Napoli, Italy.

Abstract: 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.

DOI: 10.3233/ASY-1993-6304

Journal: Asymptotic Analysis, vol. 6, no. 3, pp. 271-284, 1993