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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 149, Pages 95–102 (Mi into322)  

This article is cited in 5 scientific papers (total in 5 papers)

Riemann–Hilbert Problem for First-Order Elliptic Systems with Constant Leading Coefficients on the Plane

A. P. Soldatova, O. V. Chernovab

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
b National Research University "Belgorod State University"
Full-text PDF (193 kB) Citations (5)
References:
Abstract: In a finite domain D of the complex plane bounded by a smooth contour Γ, we consider the Riemann–Hilbert boundary-value problem
ReCU+=f
for the first-order elliptic system
UyAUx+a(z)U(z)+b(z)¯U(z)=F(z)
with constant leading coefficients. Here + denotes the boundary value of the function U on Γ, the constant matrices A1,A2Cl×l and (l×l)-matrix coefficients a and b belong to the Hölder class Cμ, 0<μ<1, and (l×l)-matrix function C belongs to the class Cμ(Γ). We prove that in the class UCμ(¯D)C1(D), this problem is a Fredholm problem and its index is given by the formula
ϰ=mj=11π[argdetG]Γj+(2m)l.
Keywords: elliptic systems, Riemann–Hilbert problem, index formula, Fredholm operator.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.7311.2017/БЧ
This work was supported by the Ministry of Education and Science of the Russian Federation (project No. 1.7311.2017/BCh).
English version:
Journal of Mathematical Sciences (New York), 2020, Volume 250, Issue 5, Pages 811–818
DOI: https://doi.org/10.1007/s10958-020-05046-y
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35Jxx, 58J10, 58J20
Language: Russian
Citation: A. P. Soldatov, O. V. Chernova, “Riemann–Hilbert Problem for First-Order Elliptic Systems with Constant Leading Coefficients on the Plane”, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 149, VINITI, Moscow, 2018, 95–102; J. Math. Sci. (N. Y.), 250:5 (2020), 811–818
Citation in format AMSBIB
\Bibitem{SolChe18}
\by A.~P.~Soldatov, O.~V.~Chernova
\paper Riemann--Hilbert Problem for First-Order Elliptic Systems with Constant Leading Coefficients on the Plane
\inbook Proceedings of the International Conference ``Actual Problems of Applied Mathematics and Physics,'' Kabardino-Balkaria, Nalchik, May 17--21, 2017
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 149
\pages 95--102
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into322}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3847728}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2020
\vol 250
\issue 5
\pages 811--818
\crossref{https://doi.org/10.1007/s10958-020-05046-y}
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  • https://www.mathnet.ru/eng/into/v149/p95
  • This publication is cited in the following 5 articles:
    1. Ali Darya, Nasir Taghizadeh, “SCHWARZ AND DIRICHLET PROBLEMS FOR COMPLEX PARTIAL DIFFERENTIAL EQUATIONS IN THE PARTIAL ECLIPSE DOMAIN”, J Math Sci, 2024  crossref
    2. A. P. Soldatov, “On a boundary problem for a fourth-order elliptic equation on a plane”, Comput. Math. Math. Phys., 62:4 (2022), 599–607  mathnet  mathnet  crossref  crossref  scopus
    3. A. P. Soldatov, O. V. Chernova, “Zadacha lineinogo sopryazheniya dlya ellipticheskikh sistem na ploskosti”, Materialy mezhdunarodnoi konferentsii po matematicheskomu modelirovaniyu v prikladnykh naukakh “International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19”. Belgorod, 20–24 avgusta 2019 g., Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 195, VINITI RAN, M., 2021, 108–117  mathnet  crossref
    4. B. D. Koshanov, A. P. Soldatov, “O razreshimosti obobschennoi zadachi Neimana dlya ellipticheskogo uravneniya vysokogo poryadka v beskonechnoi oblasti”, Posvyaschaetsya 70-letiyu prezidenta RUDN V.M. Filippova, SMFN, 67, no. 3, Rossiiskii universitet druzhby narodov, M., 2021, 564–575  mathnet  crossref
    5. S. P. Mitin, A. P. Soldatov, “Solution of the Dirichlet Problem for the Inhomogeneous Lamé System with Lower Order Coefficients”, J Math Sci, 255:6 (2021), 732  crossref
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    Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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