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

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.

DOI: https://doi.org/10.4213/sm357

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

Bibliographic databases:

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

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
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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. A. Yu. Savin, B. Yu. Sternin, “Elliptic operators in even subspaces”, Sb. Math., 190:8 (1999), 1195–1228
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3. A. Yu. Savin, B. Yu. Sternin, “Elliptic operators in odd subspaces”, Sb. Math., 191:8 (2000), 1191–1213
4. Savin, AY, “To the problem of homotopy classification of the elliptic boundary value problems”, Doklady Mathematics, 63:2 (2001), 174
5. Schulze, BW, “An algebra of boundary value problems not requiring Shapiro-Lopatinskij conditions”, Journal of Functional Analysis, 179:2 (2001), 374
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
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8. Savin, A, “Elliptic operators in subspaces and the eta invariant”, K-Theory, 27:3 (2002), 253
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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
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
14. Timothy Nguyen, “Anisotropic function spaces and elliptic boundary value problems”, Math. Nachr, 2012, n/a
15. Jörg Seiler, “Ellipticity in pseudodifferential algebras of Toeplitz type”, Journal of Functional Analysis, 2012
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17. Krainer T., Mendoza G.A., “Boundary value problems for first order elliptic wedge operators”, Am. J. Math., 138:3 (2016), 585–656
18. Schulze B.-W., Seiler J., “Elliptic Complexes on Manifolds With Boundary”, J. Geom. Anal., 29:1 (2019), 656–706
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