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Contemporary Mathematics. Fundamental Directions
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Contemporary Mathematics. Fundamental Directions, 2017, Volume 63, Issue 1, Pages 1–189
DOI: https://doi.org/10.22363/2413-3639-2017-63-1-1-189
(Mi cmfd316)
 

This article is cited in 18 scientific papers (total in 18 papers)

Singular integral operators and elliptic boundary-value problems. I

A. P. Soldatov

National Research University “Belgorod State University”, Department of Differential Equations, 85 Pobedy st., 308015 Belgorod, Russia
References:
Abstract: The book consists of three Parts I–III and Part I is presented here. In this book, we develop a new approach mainly based on the author's papers. Many results are published here for the first time.
Chapter 1 is introductory. The necessary background from functional analysis is given there for completeness. In this book, we mostly use weighted Hölder spaces, and they are considered in Ch. 2. Chapter 3 plays the main role: in weighted Hölder spaces we consider there estimates of integral operators with homogeneous difference kernels, which cover potential-type integrals and singular integrals as well as Cauchy-type integrals and double layer potentials. In Ch. 4, analogous estimates are established in weighted Lebesgue spaces.
Integrals with homogeneous difference kernels will play an important role in Part III of the monograph, which will be devoted to elliptic boundary-value problems. They naturally arise in integral representations of solutions of first-order elliptic systems in terms of fundamental matrices or their parametrixes. Investigation of boundary-value problems for second-order and higher-order elliptic equations or systems is reduced to first-order elliptic systems.
Bibliographic databases:
Document Type: Article
UDC: 517.968
Language: Russian
Citation: A. P. Soldatov, “Singular integral operators and elliptic boundary-value problems. I”, Functional analysis, CMFD, 63, no. 1, Peoples' Friendship University of Russia, M., 2017, 1–189
Citation in format AMSBIB
\Bibitem{Sol17}
\by A.~P.~Soldatov
\paper Singular integral operators and elliptic boundary-value problems.~I
\inbook Functional analysis
\serial CMFD
\yr 2017
\vol 63
\issue 1
\pages 1--189
\publ Peoples' Friendship University of Russia
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd316}
\crossref{https://doi.org/10.22363/2413-3639-2017-63-1-1-189}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3646636}
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  • This publication is cited in the following 18 articles:
    1. A. B. Rasulov, N. V. Yakivchik, “Zadacha lineinogo sopryazheniya dlya uravneniya Koshi—Rimana s silnoi osobennostyu v mladshem koeffitsiente v oblasti s kusochno gladkoi granitsei”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXIV», Voronezh, 3-9 maya 2023 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 231, VINITI RAN, M., 2024, 115–123  mathnet  crossref
    2. A. B. Rasulov, Yu. S. Fedorov, A. M. Sergeeva, “Zadachi tipa Rimana—Gilberta dlya obobschennogo uravneniya Koshi—Rimana s mladshim koeffitsientom, imeyuschim osobennost v okruzhnosti”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXIV», Voronezh, 3-9 maya 2023 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 232, VINITI RAN, M., 2024, 89–98  mathnet  crossref
    3. A. B. Rasulov, Yu. S. Fedorov, “On a statement of the boundary value problem for a generalized Cauchy–Riemann equation with nonisolated singularities in a lower-order coefficient”, Math. Notes, 116:1 (2024), 119–129  mathnet  crossref  crossref
    4. V. P. Burskii, “On weak solutions of boundary value problems for some general differential equations”, Izv. Math., 87:5 (2023), 891–905  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Bliev N.K., “Multidimensional Singular Integrals and Integral Equations in Fractional Spaces, II”, Complex Var. Elliptic Equ., 67:4 (2022), 921–931  crossref  mathscinet  isi  scopus
    6. A. P. Soldatov, “Singular integral operators with a generalized Cauchy kernel”, Dokl. Math., 105:2 (2022), 117–122  mathnet  crossref  crossref  mathscinet  elib
    7. A. Polosin, N. Popivanov, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2528, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2022, 030004  crossref
    8. A. P. Soldatov, “Ob integrale Pompeyu i nekotorykh ego obobscheniyakh”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 14:1 (2021), 60–74  mathnet  crossref
    9. 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
    10. 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
    11. A. P. Soldatov, “On moisil-theodoresko system in a complex form”, Math. Meth. Appl. Sci., 43:16, SI (2020), 9509–9521  crossref  mathscinet  zmath  isi  scopus
    12. A. P. Soldatov, “O zadache Shvartsa dlya sistemy Moisila—Teodoresko”, Differentsialnye uravneniya i matematicheskoe modelirovanie, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 188, VINITI RAN, M., 2020, 3–13  mathnet  crossref
    13. V. P. Burskii, “Generalized solutions of the linear boundary value problems”, Russian Math. (Iz. VUZ), 63:12 (2019), 21–31  mathnet  crossref  crossref  isi
    14. A. B. Rasulov, A. P. Soldatov, “Riemann-Hilbert-type problems for Bitsadze equations with strong singularities in low-order coefficients”, Complex Var. Elliptic Equ., 64:8, SI (2019), 1275–1284  crossref  mathscinet  zmath  isi  scopus
    15. S. P. Mitin, A. P. Soldatov, “On asymptotics of piecewise analytic functions”, Complex Var. Elliptic Equ., 64:5 (2019), 804–815  crossref  mathscinet  zmath  isi  scopus
    16. A. P. Soldatov, “On solvability of linear conjugation problem in weighted Holder spaces”, Proceedings of the 44Th International Conference “Applications of Mathematics in Engineering and Economics”, AIP Conf. Proc., 2048, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2018, 040003  crossref  isi  scopus
    17. 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
    18. A. P. Soldatov, “Ob odnoi kraevoi zadache dlya ellipticheskogo uravneniya vysokogo poryadka v mnogosvyaznoi oblasti na ploskosti”, Vladikavk. matem. zhurn., 19:3 (2017), 51–58  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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