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This article is cited in 11 scientific papers (total in 11 papers)
Elliptic problems with radiation conditions on edges of the boundary
S. A. Nazarov, B. A. Plamenevskii
Abstract:
A study is made of formulations of elliptic boundary value problems connected with the addition of radiation conditions on edges of the piecewise smooth boundary $\partial G$ of a domain
$G\subset\mathbb{R}^n$. Such formulations lead to Fredholm operators acting in suitable function spaces with weighted norms. The basic means of description is the generalized Green formula, which contains in addition to the usual boundary integrals also integrals over an edge $M$ of bilinear expressions formed by the coefficients of the asymptotics of the solutions near $M$. Thus, the edge and the $(n-1)$-dimensional smooth part of the boundary are on the same footing-both $M$ and $\partial G\setminus M$ are represented by their contributions to the generalized Green formula. This permits the construction of a theory of elliptic problems in which the generalized Green formula takes the role of the usual Green formula in the smooth situation.
Received: 12.04.1991
Citation:
S. A. Nazarov, B. A. Plamenevskii, “Elliptic problems with radiation conditions on edges of the boundary”, Mat. Sb., 183:10 (1992), 13–44; Russian Acad. Sci. Sb. Math., 77:1 (1994), 149–176
Linking options:
https://www.mathnet.ru/eng/sm1078https://doi.org/10.1070/SM1994v077n01ABEH003434 https://www.mathnet.ru/eng/sm/v183/i10/p13
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Abstract page: | 556 | Russian version PDF: | 193 | English version PDF: | 7 | References: | 75 | First page: | 3 |
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