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Mathematics of the USSR-Izvestiya, 1992, Volume 39, Issue 2, Pages 1033–1061
DOI: https://doi.org/10.1070/IM1992v039n02ABEH002236
(Mi im981)
 

This article is cited in 20 scientific papers (total in 20 papers)

A function theory method in boundary value problems in the plane. I. The smooth case

A. P. Soldatov

Vladimir State Pedagogical University
References:
Abstract: A general (not necessarily local) boundary value problem is considered for an elliptic (l×l) system on the plane of nth order containing only leading terms with constant coefficients. By a method of function theory developed for elliptic (s×s) systems of first order
ΦyJΦx=0
with a constant triangular matrix J=(Jij)1s, ImJij>0; this problem is reduced to an equivalent system of integrofunctional equations on the boundary. In particular, a criterion that the problem be Noetherian and a formula for its index are obtained in this way. All considerations are carried out in the smooth case when the boundary of the domain has no corner points, while the boundary operators act in spaces of continuous functions.
Received: 29.05.1990
Bibliographic databases:
UDC: 517.9
MSC: Primary 35J55; Secondary 35M99
Language: English
Original paper language: Russian
Citation: A. P. Soldatov, “A function theory method in boundary value problems in the plane. I. The smooth case”, Math. USSR-Izv., 39:2 (1992), 1033–1061
Citation in format AMSBIB
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\by A.~P.~Soldatov
\paper A function theory method in boundary value problems in the plane. I.~The~smooth case
\jour Math. USSR-Izv.
\yr 1992
\vol 39
\issue 2
\pages 1033--1061
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Linking options:
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  • https://doi.org/10.1070/IM1992v039n02ABEH002236
  • https://www.mathnet.ru/eng/im/v55/i5/p1070
    Cycle of papers
    This publication is cited in the following 20 articles:
    1. S. Aghekyan, “On a Riemann Boundary Value Problem in the Space of p-Summable Functions with Infinite Index”, J. Contemp. Mathemat. Anal., 57:6 (2022), 323  crossref
    2. M. Otelbaev, A. P. Soldatov, “Integral representations of vector functions based on the parametrix of first-order elliptic systems”, Comput. Math. Math. Phys., 61:6 (2021), 964–973  mathnet  mathnet  crossref  crossref  isi  scopus
    3. Alexandre Soldatov, INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020), 2325, INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020), 2021, 020025  crossref
    4. A. H. Babayan, “On a Dirichlet problem for one improperly elliptic equation”, Complex Variables and Elliptic Equations, 64:5 (2019), 825  crossref
    5. Armenak H. Babayan, Seyran H. Abelyan, Springer Proceedings in Mathematics & Statistics, 291, Modern Methods in Operator Theory and Harmonic Analysis, 2019, 317  crossref
    6. 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
    7. A. P. Soldatov, O. V. Chernova, “Riemann–Hilbert Problem for First-Order Elliptic Systems with Constant Leading Coefficients on the Plane”, J. Math. Sci. (N. Y.), 250:5 (2020), 811–818  mathnet  crossref  mathscinet
    8. N. Manjavidze, “Riemann–Hilbert Problems on a Cut Plane”, J Math Sci, 235:5 (2018), 632  crossref
    9. A. P. Soldatov, “K teorii anizotropnoi ploskoi uprugosti”, Trudy Sedmoi Mezhdunarodnoi konferentsii po differentsialnym i funktsionalno-differentsialnym uravneniyam (Moskva, 22–29 avgusta, 2014). Chast 3, SMFN, 60, RUDN, M., 2016, 114–163  mathnet
    10. A. P. Soldatov, “Generalized potentials of double layer in plane theory of elasticity”, Eurasian Math. J., 5:2 (2014), 78–125  mathnet
    11. A. Soldatov, “The Neumann problem for elliptic systems on a plane”, Journal of Mathematical Sciences, 202:6 (2014), 897–910  mathnet  crossref
    12. 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
    13. 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
    14. A. P. Soldatov, “Second-order elliptic systems in the half-plane”, Izv. Math., 70:6 (2006), 1233–1264  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    15. Soldatov A.P., “The Bitsadze-Samarskii problem for Douglis analytic functions”, Differential Equations, 41:3 (2005), 416–428  mathnet  crossref  mathscinet  zmath  isi  elib
    16. V. A. Oganyan, “Zadacha Dirikhle dlya slabo svyazannykh ellipticheskikh differentsialnykh uravnenii vtorogo poryadka s razryvnymi granichnymi usloviyami”, Uch. zapiski EGU, ser. Fizika i Matematika, 2003, no. 3, 16–24  mathnet
    17. Soldatov A.P., “The algebra of singular operators with terminal symbol on a piecewise smooth curve: II. Basic constructions”, Differential Equations, 37:6 (2001), 866–879  mathnet  crossref  mathscinet  zmath  isi  elib
    18. M. M. Sirazhudinov, “Boundary-value problems for general elliptic systems in the plane”, Izv. Math., 61:5 (1997), 1031–1068  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    19. Mitin S. Soldatov A., “Solvability of the Generalized Mixed Problem”, Differ. Equ., 32:3 (1996), 388–392  mathnet  mathscinet  zmath  isi
    20. 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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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