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Mat. Sb., 1998, Volume 189, Number 10, Pages 145–159 (Mi msb357)  

This article is cited in 18 scientific papers (total in 18 papers)

On general boundary-value problems for elliptic equations

B. Yu. Sternina, V. E. Shatalova, B.-W. Schulzeb

a M. V. Lomonosov Moscow State University
b University of Potsdam

Abstract: A theory of general boundary-value problems is developed for differential operators with symbols not necessarily satisfying the Atiyah–Bott condition that the corresponding obstruction must vanish. A condition ensuring that these problems possess the Fredholm property is introduced and the corresponding theorems are proved.


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English version:
Sbornik: Mathematics, 1998, 189:10, 1573–1586

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J**; Secondary 35P**, 35S**
Received: 14.05.1998

Citation: B. Yu. Sternin, V. E. Shatalov, B. Schulze, “On general boundary-value problems for elliptic equations”, Mat. Sb., 189:10 (1998), 145–159; Sb. Math., 189:10 (1998), 1573–1586

Citation in format AMSBIB
\by B.~Yu.~Sternin, V.~E.~Shatalov, B.~Schulze
\paper On general boundary-value problems for elliptic equations
\jour Mat. Sb.
\yr 1998
\vol 189
\issue 10
\pages 145--159
\jour Sb. Math.
\yr 1998
\vol 189
\issue 10
\pages 1573--1586

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    This publication is cited in the following articles:
    1. A. Yu. Savin, B. Yu. Sternin, “Elliptic operators in even subspaces”, Sb. Math., 190:8 (1999), 1195–1228  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Savin, AY, “Subspaces determined by pseudodifferential projection and some applications”, Doklady Akademii Nauk, 371:4 (2000), 448  mathnet  mathscinet  zmath  isi
    3. A. Yu. Savin, B. Yu. Sternin, “Elliptic operators in odd subspaces”, Sb. Math., 191:8 (2000), 1191–1213  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Savin, AY, “To the problem of homotopy classification of the elliptic boundary value problems”, Doklady Mathematics, 63:2 (2001), 174  mathnet  mathscinet  zmath  isi  elib
    5. Schulze, BW, “An algebra of boundary value problems not requiring Shapiro-Lopatinskij conditions”, Journal of Functional Analysis, 179:2 (2001), 374  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Savin A., Schulze B.W., Sternin B., “On the homotopy classification of elliptic boundary value problems”, Partial Differential Equations and Spectral Theory, Operator Theory : Advances and Applications, 126, 2001, 299–305  mathscinet  zmath  isi
    7. Schulze B.W., “Operator algebras with symbol hierarchies on manifolds with singularities”, Approaches to Singular Analysis - a Volume of Advances in Partial Differential Equations, Operator Theory : Advances and Applications, 125, 2001, 167–207  mathscinet  zmath  isi
    8. Savin, A, “Elliptic operators in subspaces and the eta invariant”, K-Theory, 27:3 (2002), 253  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. Schulze, BW, “Boundary value problems with global projection conditions”, Journal of Functional Analysis, 206:2 (2004), 449  crossref  mathscinet  zmath  isi  scopus  scopus
    10. Savin, A, “Boundary value problems on manifolds with fibered boundary”, Mathematische Nachrichten, 278:11 (2005), 1297  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    11. Schulze, BW, “Edge operators with conditions of Toeplitz type”, Journal of the Institute of Mathematics of Jussieu, 5:1 (2006), 101  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. Savin A., Sternin B., “Pseudo differential subspaces and their applications in elliptic theory”, C(star)-Algebras and Elliptic Theory, Trends in Mathematics, 2006, 247–289  crossref  mathscinet  zmath  adsnasa  isi
    13. Schulze B.-W., “Pseudo-differential calculus on manifolds with geometric singularities”, Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis, Fields Institute Communications, 52, 2007, 37–83  mathscinet  isi
    14. Timothy Nguyen, “Anisotropic function spaces and elliptic boundary value problems”, Math. Nachr, 2012, n/a  crossref  mathscinet  isi  scopus  scopus  scopus
    15. Jörg Seiler, “Ellipticity in pseudodifferential algebras of Toeplitz type”, Journal of Functional Analysis, 2012  crossref  mathscinet  isi  scopus  scopus  scopus
    16. Jörg Seiler, “Parameter-dependent pseudodifferential operators of Toeplitz type”, Annali di Matematica, 2013  crossref  mathscinet  scopus  scopus  scopus
    17. Krainer T., Mendoza G.A., “Boundary value problems for first order elliptic wedge operators”, Am. J. Math., 138:3 (2016), 585–656  crossref  mathscinet  zmath  isi  scopus
    18. Schulze B.-W., Seiler J., “Elliptic Complexes on Manifolds With Boundary”, J. Geom. Anal., 29:1 (2019), 656–706  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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