Nazarov, S. A.; Plamenevskij, B. A. 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) Cited in 4 Documents MSC: 35J25 Boundary value problems for second-order elliptic equations Keywords:radiation conditions on boundary edges; domain with ribs; Fredholm property PDFBibTeX XMLCite \textit{S. A. Nazarov} and \textit{B. A. Plamenevskij}, St. Petersbg. Math. J. 4, No. 3, 569--594 (1992; Zbl 0806.35027); translation from Algebra Anal. 4, No. 3, 196--225 (1992)