Abstract:
The Dirichlet problem is considered for an elliptic selfadjoint operator $L$ in a domain $D^{(s)}=D\setminus\bigcup_{i=1}^s F_i^{(s)}$, where $D$ is a bounded domain in $R_n$ and the $F_i^{(s)}$ are nonintersecting closed sets (grains). It is shown that, if the grain diameters tend to zero, and the number $s$ 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 $D$.
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