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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 6, Pages 161–192 (Mi izv692)  

This article is cited in 6 scientific papers (total in 6 papers)

Second-order elliptic systems in the half-plane

A. P. Soldatov

Belgorod State University

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.

DOI: https://doi.org/10.4213/im692

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English version:
Izvestiya: Mathematics, 2006, 70:6, 1233–1264

Bibliographic databases:

UDC: 517.9
MSC: 47G10, 45E05, 47B38
Received: 07.12.2004

Citation: A. P. Soldatov, “Second-order elliptic systems in the half-plane”, Izv. RAN. Ser. Mat., 70:6 (2006), 161–192; Izv. Math., 70:6 (2006), 1233–1264

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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. 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
    2. 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
    3. A. Soldatov, “The Neumann problem for elliptic systems on a plane”, Journal of Mathematical Sciences, 202:6 (2014), 897–910  mathnet  crossref
    4. A. P. Soldatov, “Generalized potentials of double layer in plane theory of elasticity”, Eurasian Math. J., 5:2 (2014), 78–125  mathnet
    5. 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
    6. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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