This article is cited in 3 papers

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

L. Shimon


Abstract: 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 $\Omega_r\subset\Omega$.
Bibliography: 6 titles.

UDC: 517.946.9

MSC: Primary 35J40, 35A35; Secondary 35B45

Received: 13.09.1972

 English version: Mathematics of the USSR-Sbornik, 1973, 20:4, 506–518

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