Abstract:
Asymptotic expansions (as ε→0) of solutions of the Dirichlet problem are obtained for a strongly elliptic equation of order 2m in a subdomain of Rn minus an ε-neighborhood of a smooth submanifold, without boundary, of positive codimension.
Bibliography: 18 titles.
Citation:
V. G. Maz'ya, S. A. Nazarov, B. A. Plamenevskii, “Asymptotics of solutions of the Dirichlet problem in a domain with a truncated thin tube”, Math. USSR-Sb., 44:2 (1983), 167–194
\Bibitem{MazNazPla81}
\by V.~G.~Maz'ya, S.~A.~Nazarov, B.~A.~Plamenevskii
\paper Asymptotics of solutions of the Dirichlet problem in a~domain with a~truncated thin tube
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 2
\pages 167--194
\mathnet{http://mi.mathnet.ru/eng/sm2457}
\crossref{https://doi.org/10.1070/SM1983v044n02ABEH000959}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=637860}
\zmath{https://zbmath.org/?q=an:0502.35017|0473.35019}
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This publication is cited in the following 26 articles:
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
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V. A. Kozlov, S. A. Nazarov, “Asymptotic model of interaction of blood flow with vein walls and the surrounding muscular tissue”, Dokl. Phys, 57:10 (2012), 411
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Ivan Argatov, Igor Sevostianov, “Rigid toroidal inhomogeneity in an elastic medium”, International Journal of Engineering Science, 49:1 (2011), 61
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E. Yu. Postnikova, “Asimptotika kraevoi zadachi v oblasti s
dvumya otverstiyami”, Vestnik ChelGU, 2011, no. 13, 49–58
Ivan I. Argatov, Federico J. Sabina, “Acoustic diffraction by a thin soft torus”, Wave Motion, 45:6 (2008), 846
I. I. Argatov, “Asymptotics of the reduced logarithmic capacity of a narrow cylinder”, Math. Notes, 77:1 (2005), 15–25
I. I. Argatov, “Asymptotics of a reduced logarithmic capacity”, Comput. Math. Math. Phys., 45:1 (2005), 120–137
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Argatov I., “Pressure of a Narrow Band-Like Punch Upon an Elastic Half-Space”, Int. Appl. Mech., 36:10 (2000), 1363–1368
R. R. Gadyl'shin, “Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator”, Russian Math. Surveys, 52:1 (1997), 1–72
I. I. Argatov, S. A. Nazarov, “Asymptotic solution of the Signorini problem with an obstacle on a thin elongated set”, Sb. Math., 187:10 (1996), 1411–1442
I. I. Argatov, S. A. Nazarov, “Asymptotic analysis of problems on junctions of domains of different limit dimensions. A body pierced by a thin rod”, Izv. Math., 60:1 (1996), 1–37
Argatov I., Nazarov S., “The Pressure of a Narrow Ring-Shaped Punch on an Elastic Half-Space”, Pmm-J. Appl. Math. Mech., 60:5 (1996), 799–812
Argatov I., Nazarov S., “Junction Problem of Shashlik (Skewer) Type”, Comptes Rendus Acad. Sci. Ser. I-Math., 316:12 (1993), 1329–1334
I. Yu. Popov, “The Helmholtz resonator and the theory of operator extensions in a space with indefinite metric”, Russian Acad. Sci. Sb. Math., 75:2 (1993), 285–315
I. Yu. Popov, “Extension theory and localization of resonances for domains of trap type”, Math. USSR-Sb., 71:1 (1992), 209–234
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