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Selfadjoint elliptic problems with radiation conditions on the edges of the boundary. (English. Russian original) Zbl 0806.35027

St. Petersbg. Math. J. 4, No. 3, 569-594 (1993); translation from Algebra Anal. 4, No. 3, 196-225 (1992).
This article deals with the elliptic equation \({\mathcal L} (x,D_ x) u(x) = f(x)\) \((x \in G)\) in a domain \(G\) with ribs \(M\) under boundary conditions \({\mathcal B} (x,D_ x) u(x) = g(x)\) \((x \in \partial G \backslash M)\) and some special boundary conditions on \(M\) that ensure formal self- adjointness of the linear operator \(({\mathcal L}, {\mathcal B})\). The main result formulates some natural conditions ‘of radiation on ribs’, that guarantee the Fredholm property for \(({\mathcal L}, {\mathcal B})\); physical sense of these conditions is presented, too.
Reviewer: P.Zabreiko (Minsk)

MSC:

35J25 Boundary value problems for second-order elliptic equations
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