ASYMPTOTIC EXPANSIONS OF EIGENELEMENTS OF THE LAPLACE OPERATOR IN A DOMAIN WITH MANY 'LIGHT' CONCENTRATED MASSES CLOSELY LOCATED ON THE BOUNDARY. MULTI-DIMENSIONAL CASE

摘要

A spectral problem for the Laplace operator is considered in a domain with singular density near the boundary (with concentrated masses). The boundary condition is of rapidly variable type. We construct asymptotic expansions for the eigenvalues and eigenfunctions of the problem with respect to a small parameter characterizing the diameter and density of masses, as well as distance between the masses. The expansions are justified.