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Mat. Sb., 1994, Volume 185, Number 3, Pages 117–159 (Mi msb888)  

This article is cited in 17 scientific papers (total in 17 papers)

Transfer of an extension of the algebra of pseudodifferential operators, and some nonlocal elliptic problems

B. Yu. Sternin, V. E. Shatalov

M. V. Lomonosov Moscow State University

Abstract: Finiteness theorems (the Fredholm property) are proved in this paper for a certain class of elliptic problems. The operators corresponding to these problems are obtained as the elements of an extension of the set of pseudodifferential operators via a special class of (nonlocal) operators.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 81:2, 363–396

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J40, 58G20, 35S15; Secondary 47G30, 47A60, 58G15
Received: 22.04.1993

Citation: B. Yu. Sternin, V. E. Shatalov, “Transfer of an extension of the algebra of pseudodifferential operators, and some nonlocal elliptic problems”, Mat. Sb., 185:3 (1994), 117–159; Russian Acad. Sci. Sb. Math., 81:2 (1995), 363–396

Citation in format AMSBIB
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\paper Transfer of an extension of the~algebra of pseudodifferential operators, and some nonlocal elliptic problems
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 3
\pages 117--159
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\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 81
\issue 2
\pages 363--396
\crossref{https://doi.org/10.1070/SM1995v081n02ABEH003543}
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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. B. Yu. Sternin, V. E. Shatalov, “Relative elliptic theory and the Sobolev problem”, Sb. Math., 187:11 (1996), 1691–1720  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Korovina M., “On Zeta-Function of Operators Associated with the Smooth Manifolds”, Dokl. Akad. Nauk, 368:1 (1999), 10–13  mathnet  mathscinet  zmath  isi
    3. Korovina M., “Investigation of the Zeta-Function of Operators Corresponding to a Class of Nonlocal Elliptic Problems”, Differ. Equ., 35:8 (1999), 1077–1086  mathnet  mathscinet  zmath  isi
    4. Korovina M., “On Self-Adjoint Extension of Schrodinger Operator with Potential Concentrated of the Smooth Manifold”, Dokl. Akad. Nauk, 366:6 (1999), 738–740  mathnet  mathscinet  zmath  isi
    5. Korovina M., “The Construction of a Self-Adjoint Extension of the Schro-Dinger Operator with Potential Concentrated on a Pencil of Planes: I”, Differ. Equ., 38:6 (2002), 816–829  mathnet  crossref  mathscinet  zmath  isi
    6. Korovina M., “Construction of a Self-Adjoint Extension of the Schrodinger Operator with a Potential Concentrated on a Pencil of Planes: II”, Differ. Equ., 39:1 (2003), 73–82  mathnet  crossref  mathscinet  zmath  isi
    7. Korovina M., “Elliptic Problems on Stratified Manifolds in Spaces with Asymptotics: II”, Differ. Equ., 40:6 (2004), 827–838  mathnet  crossref  mathscinet  zmath  isi
    8. Korovina M., “Elliptic Problems on Stratified Manifolds in Spaces with Asymptotics: I”, Differ. Equ., 40:2 (2004), 227–240  mathnet  crossref  mathscinet  zmath  isi
    9. A. L. Skubachevskii, “Nonclassical boundary value problems. I”, Journal of Mathematical Sciences, 155:2 (2008), 199–334  mathnet  crossref  mathscinet  zmath  elib
    10. Korovina, MV, “Relative elliptic operators and the Sobolev problem: II”, Differential Equations, 43:4 (2007), 525  crossref  mathscinet  zmath  isi  elib
    11. Korovina M.V., “Relative Elliptic Operators and the Sobolev Problem: I”, Differ. Equ., 43:3 (2007), 381–395  crossref  mathscinet  zmath  isi  elib
    12. Korovina M.V., “The Algebra of Relative Morphisms on Stratified Manifolds”, Dokl. Math., 75:1 (2007), 108–111  crossref  mathscinet  isi  elib
    13. Korovina, MV, “Relative elliptic morphisms and some of their applications”, Doklady Mathematics, 77:2 (2008), 226  crossref  mathscinet  zmath  isi  elib
    14. Korovina M.V., “Sobolev Problem on a Stratified Manifold”, Differ. Equ., 44:1 (2008), 115–123  crossref  mathscinet  zmath  isi  elib
    15. A. L. Skubachevskii, “Nonclassical boundary-value problems. II”, Journal of Mathematical Sciences, 166:4 (2010), 377–561  mathnet  crossref  mathscinet  elib
    16. Boris Yu. Sternin, “On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem”, centr.eur.j.math, 2011  crossref
    17. A. Yu. Savin, B. Yu. Sternin, “On the index of nonlocal elliptic operators associated with fibrations”, Dokl. Math, 89:1 (2014), 61  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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