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Mat. Sb., 1996, Volume 187, Number 11, Pages 115–144 (Mi msb174)  

This article is cited in 9 scientific papers (total in 9 papers)

Relative elliptic theory and the Sobolev problem

B. Yu. Sternin, V. E. Shatalov


Abstract: An operator algebra associated with a smooth embedding $i \colon X\hookrightarrow M$ is constructed. For elliptic elements of this algebra a finiteness theorem (the Fredholm property) is established, and the index is computed. A connection with Sobolev problems is shown.

DOI: https://doi.org/10.4213/sm174

Full text: PDF file (364 kB)
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English version:
Sbornik: Mathematics, 1996, 187:11, 1691–1720

Bibliographic databases:

UDC: 517.9
MSC: Primary 58G15; Secondary 58G03, 47A53, 47G30, 35S30, 35S15
Received: 26.04.1995

Citation: B. Yu. Sternin, V. E. Shatalov, “Relative elliptic theory and the Sobolev problem”, Mat. Sb., 187:11 (1996), 115–144; Sb. Math., 187:11 (1996), 1691–1720

Citation in format AMSBIB
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\paper Relative elliptic theory and the~Sobolev problem
\jour Mat. Sb.
\yr 1996
\vol 187
\issue 11
\pages 115--144
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  • http://mi.mathnet.ru/eng/msb/v187/i11/p115

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Nazaikinskii, VE, “On the Green operator in relative elliptic theory”, Doklady Mathematics, 68:1 (2003), 57  mathscinet  zmath  isi  elib
    2. Korovina, MV, “Relative elliptic operators and the Sobolev problem: II”, Differential Equations, 43:4 (2007), 525  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. Korovina, MV, “Relative elliptic morphisms and some of their applications”, Doklady Mathematics, 77:2 (2008), 226  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. Nguen L.L., “Zadachi soboleva dlya deistvii konechnykh grupp”, Trudy moskovskogo fiziko-tekhnicheskogo instituta, 2012, 125–133  elib
    5. A. Yu. Savin, B. Yu. Sternin, “On the index of nonlocal elliptic operators associated with fibrations”, Dokl. Math, 89:1 (2014), 61  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    6. Yu. A. Kordyukov, V. A. Pavlenko, “Singular integral operators on a manifold with a distinguished submanifold”, Ufa Math. J., 6:3 (2014), 35–68  mathnet  crossref  elib
    7. Savin A.Yu., Sternin B.Yu., “Index of Sobolev Problems on Manifolds With Many-Dimensional Singularities”, Differ. Equ., 50:2 (2014), 232–245  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    8. Loshchenova D.A., “Sobolev Problems Associated With Lie Group Actions”, Differ. Equ., 51:8 (2015), 1051–1064  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    9. P. A. Sipailo, “On Traces of Fourier Integral Operators on Submanifolds”, Math. Notes, 104:4 (2018), 559–571  mathnet  crossref  crossref  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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