On the approximation of solutions of boundary value problems in domains with an unbounded boundary

Elliptic problems with a complex parameter $q$ are considered for equations with variable coefficients in domains $\Omega$ with an unbounded boundary. It is proved that for sufficiently large $|q|$ the problem has a unique solution in the space $H^s(\Omega)$ and that the solution can be obtained as the limit as $r\to\infty$ of the solution of a boundary value problem in a certain bounded domain $\Omega_r\subset\Omega$.
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