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Izvestiya: Mathematics, 2006, Volume 70, Issue 6, Pages 1233–1264
DOI: https://doi.org/10.1070/IM2006v070n06ABEH002345
(Mi im692)
 

This article is cited in 15 scientific papers (total in 15 papers)

Second-order elliptic systems in the half-plane

A. P. Soldatov

Belgorod State University
References:
Abstract: We consider boundary-value problems in the upper half-plane for second-order elliptic systems with constant higher coefficients. Using the Bitsadze transformation, we reduce these problems to equivalent problems for analytic functions. This approach enables us to obtain explicit formulae for the solutions of basic boundary-value problems and to study the Fredholm solubility of these problems. (In particular, we obtain an analytic expression for the index.) We work in weighted Hölder and Hardy spaces.
Received: 07.12.2004
Bibliographic databases:
UDC: 517.9
MSC: 47G10, 45E05, 47B38
Language: English
Original paper language: Russian
Citation: A. P. Soldatov, “Second-order elliptic systems in the half-plane”, Izv. Math., 70:6 (2006), 1233–1264
Citation in format AMSBIB
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\by A.~P.~Soldatov
\paper Second-order elliptic systems in the half-plane
\jour Izv. Math.
\yr 2006
\vol 70
\issue 6
\pages 1233--1264
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Linking options:
  • https://www.mathnet.ru/eng/im692
  • https://doi.org/10.1070/IM2006v070n06ABEH002345
  • https://www.mathnet.ru/eng/im/v70/i6/p161
  • This publication is cited in the following 15 articles:
    1. A. B Rasulov, “Influence of Nonisolated Singularities in a Lower-Order Coefficient of the Bitsadze Equation on the Statement of Boundary Value Problems”, Differentsialnye uravneniya, 59:10 (2023), 1385  crossref
    2. A. B. Rasulov, “Influence of Nonisolated Singularities in a Lower-Order Coefficient of the Bitsadze Equation on the Statement of Boundary Value Problems”, Diff Equat, 59:10 (2023), 1384  crossref
    3. Zhapsarbayeva L., Ospanov K., “Solvability of Nonlinear Problem For Some Second-Order Nonstrongly Elliptic System”, Complex Var. Elliptic Equ., 66:6-7 (2021), 1073–1083  crossref  mathscinet  isi
    4. A. P. Soldatov, Trends in Mathematics, Analysis as a Life, 2019, 279  crossref
    5. Gryshchuk S.V., Plaksa S.A., “A Schwartz-Type Boundary Value Problem in a Biharmonic Plane”, Lobachevskii J. Math., 38:3, SI (2017), 435–442  crossref  mathscinet  zmath  isi  scopus
    6. A. P. Soldatov, “Mixed problem of plane orthotropic elasticity in a half-plane”, Diff Equat, 52:6 (2016), 798  crossref
    7. A. P. Soldatov, “Generalized potentials of double layer in plane theory of elasticity”, Eurasian Math. J., 5:2 (2014), 78–125  mathnet
    8. Rajabov N.R., Rasulov A.B., “Linear Transmission Problem For a Bitsadze System With a Supersingular Circle”, Differ. Equ., 50:4 (2014), 526–532  crossref  mathscinet  zmath  isi  scopus
    9. A. Soldatov, “The Neumann problem for elliptic systems on a plane”, Journal of Mathematical Sciences, 202:6 (2014), 897–910  mathnet  crossref
    10. A. B. Rasulov, “Dirichlet and Hilbert problems for elliptic systems of second and third orders with a supersingular point”, Journal of Mathematical Sciences, 189:2 (2012), 257–273  mathnet  mathnet  crossref
    11. Radzhabov N.R., Rasulov A.B., “O korrektnoi postanovke zadach dlya sistemy bitsadze so sverkhsingulyarnoi tochkoi i okruzhnostyu”, Nauchnye vedomosti belgorodskogo gosudarstvennogo universiteta, 25:23 (2011), 96–101  elib
    12. Rasulov A.B., “Zadachi tipa Dirikhle dlya nekotorykh modelnykh uravnenii ellipticheskogo tipa so sverkhsingulyarnoi tochkoi”, Vestn. Mosk. energeticheskogo in-ta, 2010, no. 6, 47–53  elib
    13. A. P. Soldatov, “Hardy space of solutions of elliptic systems on the plane”, Journal of Mathematical Sciences, 160:1 (2009), 103–115  mathnet  mathnet  crossref
    14. A. P. Soldatov, E. A. Abapolova, “Lamé system of elasticity theory in a plane orthotropic medium”, Journal of Mathematical Sciences, 157:3 (2009), 387–394  mathnet  mathnet  crossref
    15. A. P. Soldatov, “The Hardy space of solutions to first-order elliptic systems”, Dokl. Math., 76:2 (2007), 660  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:107
    First page:13
     
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