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Mat. Zametki, 2005, Volume 77, Issue 5, Pages 665–682 (Mi mz2525)  

This article is cited in 7 scientific papers (total in 7 papers)

Generalized Solutions of Nonlocal Elliptic Problems

P. L. Gurevich

Moscow Aviation Institute

Abstract: An elliptic equation of order $2m$ with general nonlocal boundary-value conditions, in a plane bounded domain $G$ with piecewise smooth boundary, is considered. Generalized solutions belonging to the Sobolev space $W_2^m(G)$ are studied. The Fredholm property of the unbounded operator (corresponding to the elliptic equation) acting on $L_2(G)$, and defined for functions from the space $W_2^m(G)$ that satisfy homogeneous nonlocal conditions, is established.

DOI: https://doi.org/10.4213/mzm2525

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English version:
Mathematical Notes, 2005, 77:5, 614–629

Bibliographic databases:

UDC: 517.9
Received: 30.03.2004

Citation: P. L. Gurevich, “Generalized Solutions of Nonlocal Elliptic Problems”, Mat. Zametki, 77:5 (2005), 665–682; Math. Notes, 77:5 (2005), 614–629

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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. P. L. Gurevich, “On the Stability of the Index of Unbounded Nonlocal Operators in Sobolev Spaces”, Proc. Steklov Inst. Math., 255 (2006), 108–126  mathnet  crossref  mathscinet  elib
    2. A. L. Skubachevskii, “Nonclassical boundary value problems. I”, Journal of Mathematical Sciences, 155:2 (2008), 199–334  mathnet  crossref  mathscinet  zmath  elib
    3. P. L. Gurevich, “On the index instability for some nonlocal elliptic problems”, J. Math. Sci. (N. Y.), 143:4 (2007), 3293–3302  mathnet  crossref  mathscinet  elib
    4. A. L. Skubachevskii, “On Necessary Conditions for the Fredholm Solvability of Nonlocal Elliptic Problems”, Proc. Steklov Inst. Math., 260 (2008), 238–253  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. Gurevich, P, “Smoothness of generalized solutions for higher-order elliptic equations with nonlocal boundary conditions”, Journal of Differential Equations, 245:5 (2008), 1323  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. A. L. Skubachevskii, “Nonclassical boundary-value problems. II”, Journal of Mathematical Sciences, 166:4 (2010), 377–561  mathnet  crossref  mathscinet  elib
    7. P. L. Gurevich, “Elliptic problems with nonlocal boundary conditions and Feller semigroups”, Journal of Mathematical Sciences, 182:3 (2012), 255–440  mathnet  crossref  mathscinet  zmath
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