THE METHOD OF ORTHOGONAL PROJECTIONS AND THE DIRICHLET PROBLEM IN DOMAINS WITH A FINE-GRAINED BOUNDARY

The Dirichlet problem is considered for an elliptic selfadjoint operator in a domain , where is a bounded domain in and the are nonintersecting closed sets (grains). It is shown that, if the grain diameters tend to zero, and the number of grains tends to infinity, the solution of the problem reduces, under certain conditions, to the solution of another boundary value problem in the simpler domain .Bibliography: 8 items.