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

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

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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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    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  isi  elib
    10. Sipailo P.A., “Traces of Quantized Canonical Transformations on Submanifolds and Their Applications to Sobolev Problems With Nonlocal Conditions”, Russ. J. Math. Phys., 26:1 (2019), 135–138  crossref  mathscinet  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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