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Mat. Sb., 1992, Volume 183, Number 10, Pages 13–44 (Mi msb1078)  

This article is cited in 10 scientific papers (total in 10 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.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 77:1, 149–176

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J55; Secondary 46E35, 26B20, 47A53
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

Citation in format AMSBIB
\by S.~A.~Nazarov, B.~A.~Plamenevskii
\paper Elliptic problems with radiation conditions on edges of the~boundary
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 10
\pages 13--44
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 1
\pages 149--176

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    This publication is cited in the following articles:
    1. Nazarov S., “Asymptotic Solutions of a Variational Inequality with Small Obstacles”, Comptes Rendus Acad. Sci. Ser. I-Math., 318:11 (1994), 1059–1064  mathscinet  zmath  isi
    2. S. A. Nazarov, “The Operator of a Boundary Value Problem With Chaplygin–Zhukovskii–Kutta Type Conditions on an Edge of the Boundary Has the Fredholm Property”, Funct. Anal. Appl., 31:3 (1997), 183–192  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. S. A. Nazarov, “The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes”, Russian Math. Surveys, 54:5 (1999), 947–1014  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. Nazarov S. Pileckas K., “On Steady Stokes and Navier–Stokes Problems with Zero Velocity at Infinity in a Three-Dimensional Exterior Domain”, J. Math. Kyoto Univ., 40:3 (2000), 475–492  mathscinet  zmath  isi
    5. S. A. Nazarov, “Elliptic Boundary Value Problems in Hybrid Domains”, Funct. Anal. Appl., 38:4 (2004), 283–297  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. S. A. Nazarov, G. H. Sweers, “Boundary value problems for the bi-harmonic equation and for the iterated Laplacian in a three-dimensional domain with an edge”, J. Math. Sci. (N. Y.), 143:2 (2007), 2936–2960  mathnet  crossref  mathscinet  zmath  elib
    7. J. Appl. Industr. Math., 3:3 (2009), 377–390  mathnet  crossref  mathscinet
    8. S. A. Nazarov, “Asymptotics of trapped modes and eigenvalues below the continuous spectrum of a waveguide with a thin shielding obstacle”, St. Petersburg Math. J., 23:3 (2012), 571–601  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    9. S. A. Nazarov, “Asymptotics of eigen-oscillations of a massive elastic body with a thin baffle”, Izv. Math., 77:1 (2013), 87–142  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. S. A. Nazarov, “Asymptotics of the eigenvalues of boundary value problems for the Laplace operator in a three-dimensional domain with a thin closed tube”, Trans. Moscow Math. Soc., 76:1 (2015), 1–53  mathnet  crossref  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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