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Russian Academy of Sciences. Izvestiya Mathematics, 1993, Volume 40, Issue 3, Pages 529–563
DOI: https://doi.org/10.1070/IM1993v040n03ABEH002176
(Mi im939)
 

This article is cited in 16 scientific papers (total in 16 papers)

A function theorety method in elliptic problems in the plane. II. The piecewise smooth case

A. P. Soldatov

Scientific Research Institute of Applied Mathematics and Automation, Kabardino-Balkar Scientific Centre of the Russian Academy of Sciences
References:
Abstract: A general boundary value problem, encompassing from a unified viewpoint a broad circle of local and nonlocal boundary value problems, is studied for elliptic systems with real, constant (and only leading) matrix coefficients. A method is given for the equivalent reduction of this problem to a system of boundary equations. The considerations are carried out in domains with piecewise smooth boundaries and in weighted spaces. A Noetherian criterion and an index formula for this problem are established, and the asymptotics of its solution in a neighborhood of corner points is described.
Received: 25.04.1991
Bibliographic databases:
UDC: 517.9
MSC: Primary 35J30; Secondary 30E25, 35B40
Language: English
Original paper language: Russian
Citation: A. P. Soldatov, “A function theorety method in elliptic problems in the plane. II. The piecewise smooth case”, Russian Acad. Sci. Izv. Math., 40:3 (1993), 529–563
Citation in format AMSBIB
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\by A.~P.~Soldatov
\paper A function theorety method in elliptic problems in the plane. II.~The piecewise smooth case
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 40
\issue 3
\pages 529--563
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\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..40..529S}
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Linking options:
  • https://www.mathnet.ru/eng/im939
  • https://doi.org/10.1070/IM1993v040n03ABEH002176
  • https://www.mathnet.ru/eng/im/v56/i3/p566
    Cycle of papers
    This publication is cited in the following 16 articles:
    1. Mitin S.P. Soldatov A.P., “Bitsadze-Samarski Problem For Elliptic Systems of Second Order”, Azerbaijan J. Math., 11:1 (2021), 154–168  isi
    2. A. H. Babayan, “On a Dirichlet problem for one improperly elliptic equation”, Complex Variables and Elliptic Equations, 64:5 (2019), 825  crossref
    3. Armenak H. Babayan, Seyran H. Abelyan, Springer Proceedings in Mathematics & Statistics, 291, Modern Methods in Operator Theory and Harmonic Analysis, 2019, 317  crossref
    4. Yu. A. Bogan, “The Dirichlet Problem for an Elliptic System of Second-Order Equations with Constant Real Coefficients in the Plane”, Math. Notes, 104:5 (2018), 636–641  mathnet  crossref  crossref  mathscinet  isi  elib
    5. S. I. Bezrodnykh, V. I. Vlasov, “Singular Riemann–Hilbert problem in complex-shaped domains”, Comput. Math. Math. Phys., 54:12 (2014), 1826–1875  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. H.M. Hayrapetyan, P.E. Meliksetyan, “On normal solvability of a Dirichlet-type problem for a third-order improperly elliptic equation”, Complex Variables and Elliptic Equations, 2011, 1  crossref
    7. Kovaleva L.A., Soldatov A.P., “On a Nonlocal Problem in Function Theory”, Differ. Equ., 46:3 (2010), 400–414  crossref  mathscinet  zmath  isi
    8. Vashchenko O.V., Soldatov A.P., “The Hardy Space of Solutions of the Generalized Beltrami System”, Differ. Equ., 43:4 (2007), 503–506  crossref  mathscinet  zmath  isi
    9. Soldatov A.P., “On the Index of the Dirichlet Problem for Elliptic Systems on the Plane”, Differ. Equ., 42:8 (2006), 1156–1169  mathnet  crossref  mathscinet  zmath  isi
    10. Soldatov A.P., “The Bitsadze-Samarskii problem for Douglis analytic functions”, Differential Equations, 41:3 (2005), 416–428  mathnet  crossref  mathscinet  zmath  isi  elib
    11. Soldatov A., “Weighted Hardy Classes of Analytic Functions”, Differ. Equ., 38:6 (2002), 855–864  mathnet  crossref  mathscinet  zmath  isi
    12. M. M. Sirazhudinov, A. G. Magomedov, V. G. Magomedova, “Boundary-value problems for general elliptic systems in the plane. II”, Izv. Math., 64:3 (2000), 601–651  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. Soldatov A., “Riemann–Hilbert Problem for the Lavrent'Ev-Bitsadze System”, Differ. Equ., 34:12 (1998), 1656–1666  mathnet  mathscinet  zmath  isi
    14. Mitin S., “Representation of Solutions of Anisotropic Elasticity”, Differ. Equ., 34:1 (1998), 95–102  mathnet  mathscinet  zmath  isi
    15. Mitin S., Soldatov A., “Solvability of the Generalized Mixed Problem”, Differ. Equ., 32:3 (1996), 388–392  mathnet  mathscinet  zmath  isi
    16. Soldatov A., “The Problems of Dirichlet Type for Lavrentev-Bitsadze Equation .2. Existence Theorems”, Dokl. Akad. Nauk, 333:1 (1993), 16–18  mathnet  mathscinet  zmath  isi
    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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    Abstract page:600
    Russian version PDF:205
    English version PDF:29
    References:83
    First page:4
     
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