RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 2016, Volume 71, Issue 5(431), Pages 3–112 (Mi umn9739)  

This article is cited in 34 scientific papers (total in 34 papers)

Boundary-value problems for elliptic functional-differential equations and their applications

A. L. Skubachevskii

RUDN University, Moscow, Russia

Abstract: Boundary-value problems are considered for strongly elliptic functional-differential equations in bounded domains. In contrast to the case of elliptic differential equations, smoothness of generalized solutions of such problems can be violated in the interior of the domain and may be preserved only on some subdomains, and the symbol of a self-adjoint semibounded functional-differential operator can change sign. Both necessary and sufficient conditions are obtained for the validity of a Gårding-type inequality in algebraic form. Spectral properties of strongly elliptic functional-differential operators are studied, and theorems are proved on smoothness of generalized solutions in certain subdomains and on preservation of smoothness on the boundaries of neighbouring subdomains. Applications of these results are found to the theory of non-local elliptic problems, to the Kato square-root problem for an operator, to elasticity theory, and to problems in non-linear optics.
Bibliography: 137 titles.

Keywords: elliptic functional-differential equations, spectral properties, smoothness of generalized solutions, non-local elliptic problems, Kato square-root problem, three-layer plates, non-linear optical systems with two-dimensional feedback.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00265
Ministry of Education and Science of the Russian Federation НШ-4479.2014.1
This research was supported by the Russian Foundation for Basic Research (grant no. 14-01-00265) and the Programme "Leading Scientific Schools" (grant no. НШ-4479.2014.1).


DOI: https://doi.org/10.4213/rm9739

Full text: PDF file (1802 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2016, 71:5, 801–906

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J25; Secondary 35B65
Received: 30.11.2015
Revised: 03.06.2015

Citation: A. L. Skubachevskii, “Boundary-value problems for elliptic functional-differential equations and their applications”, Uspekhi Mat. Nauk, 71:5(431) (2016), 3–112; Russian Math. Surveys, 71:5 (2016), 801–906

Citation in format AMSBIB
\Bibitem{Sku16}
\by A.~L.~Skubachevskii
\paper Boundary-value problems for elliptic functional-differential equations and their applications
\jour Uspekhi Mat. Nauk
\yr 2016
\vol 71
\issue 5(431)
\pages 3--112
\mathnet{http://mi.mathnet.ru/umn9739}
\crossref{https://doi.org/10.4213/rm9739}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3588929}
\zmath{https://zbmath.org/?q=an:06691824}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2016RuMaS..71..801S}
\elib{https://elibrary.ru/item.asp?id=27349997}
\transl
\jour Russian Math. Surveys
\yr 2016
\vol 71
\issue 5
\pages 801--906
\crossref{https://doi.org/10.1070/RM9739}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000394175400001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85011620405}


Linking options:
  • http://mi.mathnet.ru/eng/umn9739
  • https://doi.org/10.4213/rm9739
  • http://mi.mathnet.ru/eng/umn/v71/i5/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. E. P. Ivanova, “O koertsitivnosti differentsialno-raznostnykh uravnenii s nesoizmerimymi sdvigami argumentov”, Trudy seminara po differentsialnym i funktsionalno-differentsialnym uravneniyam v RUDN pod rukovodstvom A. L. Skubachevskogo, SMFN, 62, RUDN, M., 2016, 85–99  mathnet
    2. V. A. Popov, “Sledy obobschennykh reshenii ellipticheskikh differentsialno-raznostnykh uravnenii s vyrozhdeniem”, Trudy seminara po differentsialnym i funktsionalno-differentsialnym uravneniyam v RUDN pod rukovodstvom A. L. Skubachevskogo, SMFN, 62, RUDN, M., 2016, 124–139  mathnet
    3. A. Ashyralyev, Kh. Belakroum, A. Guezane-Lakoud, “Stability of boundary-value problems for third-order partial differential equations”, Electron. J. Differential Equations, 2017, 53, 11 pp.  mathscinet  zmath  isi
    4. A. Ashyralyev, F. Emharab, “Source identification problems for hyperbolic differential and difference equations”, International Conference Functional Analysis In Interdisciplinary Applications (FAIA 2017), AIP Conf. Proc., 1880, Amer. Inst. Phys., 2017, 040001  crossref  isi  scopus
    5. A. Ashyralyev, Kh. Belakroum, A. Guezane-Lakoud, “Numerical algorithm for the third-order partial differential equation with local boundary conditions”, International Conference Functional Analysis In Interdisciplinary Applications (FAIA 2017), AIP Conf. Proc., 1880, Amer. Inst. Phys., 2017, 040008  crossref  isi  scopus
    6. A. Ashyralyev, Kh. Belakroum, A. Guezane-Lakoud, “Numerical algorithm for the third-order partial differential equation with nonlocal boundary conditions”, International Conference Functional Analysis In Interdisciplinary Applications (FAIA 2017), AIP Conf. Proc., 1880, Amer. Inst. Phys., 2017, 040012  crossref  isi  scopus
    7. A. Muravnik, “On the half-plane Dirichlet problem for differential-difference elliptic equations with several nonlocal terms”, Math. Model. Nat. Phenom., 12:6 (2017), 130–143  crossref  zmath  isi  scopus
    8. L. Rossovskii, “Elliptic functional differential equations with incommensurable contractions”, Math. Model. Nat. Phenom., 12:6 (2017), 226–239  crossref  mathscinet  zmath  isi
    9. E. Bravyi, “Boundary value problems for families of functional differential equations”, Mem. Differ. Equ. Math. Phys., 72 (2017), 27–35  mathscinet  zmath  isi
    10. Ch. Ashyralyyev, G. Akyuz, M. Dedeturk, “Approximate solution for an inverse problem of multidimensional elliptic equation with multipoint nonlocal and Neumann boundary conditions”, Electron. J. Differential Equations, 2017, 197, 16 pp.  mathscinet  zmath  isi
    11. A. B. Muravnik, “Asimptoticheskie svoistva reshenii dvumernykh differentsialno-raznostnykh ellipticheskikh zadach”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 63, no. 4, Rossiiskii universitet druzhby narodov, M., 2017, 678–688  mathnet  crossref
    12. A. L. Skubachevskii, “The Kato conjecture for elliptic differential-difference operators with degeneration in a cylinder”, Dokl. Math., 97:1 (2018), 32–34  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    13. Kh. Belakroum, A. Ashyralyev, A. Guezane-Lakoud, “A note on the nonlocal boundary value problem for a third order partial differential equation”, Filomat, 32:3 (2018), 801–808  crossref  isi  scopus
    14. A. L. Skubachevskiǐ, “On a class of functional-differential operators satisfying the Kato conjecture”, St. Petersburg Math. J., 30:2 (2019), 329–346  mathnet  crossref  mathscinet  isi  elib
    15. O. V. Solonukha, “On an Elliptic Differential-Difference Equation with Nonsymmetric Shift Operator”, Math. Notes, 104:4 (2018), 572–586  mathnet  crossref  crossref  isi  elib
    16. A. L. Skubachevskii, “On a property of regularly accretive differential-difference operators with degeneracy”, Russian Math. Surveys, 73:2 (2018), 372–374  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    17. A. Ashyraliev, Kh. Belakrum, “Ustoichivaya raznostnaya skhema dlya uravneniya v chastnykh proizvodnykh tretego poryadka”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 1–19  mathnet  crossref
    18. V. A. Popov, “Otsenki reshenii ellipticheskikh differentsialno-raznostnykh uravnenii s vyrozhdeniem”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 131–147  mathnet  crossref
    19. A. Aibeche, N. Amroune, S. Maingot, “General non local boundary value problem for second order elliptic equation”, Math. Nachr., 291:10 (2018), 1470–1485  crossref  mathscinet  zmath  isi  scopus
    20. Ch. Ashyralyyev, A. Çay, “Well-posedness of Neumann-type elliptic overdetermined problem with integral condition”, International Conference on Analysis and Applied Mathematics (ICAAM 2018), AIP Conf. Proc., 1997, Amer. Inst. Phys., 2018, 020026-1  crossref  isi  scopus
    21. Ch. Ashyralyyev, G. Akyuz, “A third order of accuracy difference scheme for Bitsadze-Samarskii type elliptic overdetermined multi-point problem”, International Conference on Analysis and Applied Mathematics (ICAAM 2018), AIP Conf. Proc., 1997, Amer. Inst. Phys., 2018, 020009-1  crossref  isi  scopus
    22. A. L. Skubachevskii, “Elliptic differential-difference operators with degeneration and the Kato square root problem”, Math. Nachr., 291:17-18 (2018), 2660–2692  crossref  mathscinet  zmath  isi
    23. A. Ashyralyev, O. Gercek, E. Zusi, “A note on the second order of accuracy difference scheme for elliptic-parabolic equations in Holder spaces”, Bull. Karaganda Univ. Math., 91:3 (2018), 108–116  crossref  isi
    24. E. P. Ivanova, “On Smooth Solutions of Differential-Difference Equations with Incommensurable Shifts of Arguments”, Math. Notes, 105:1 (2019), 140–144  mathnet  crossref  crossref  isi  elib
    25. Skubachevskii A.L., Liiko V.V., “On a Certain Property of a Regular Difference Operator With Variable Coefficients”, Complex Var. Elliptic Equ., 64:5 (2019), 852–865  crossref  mathscinet  zmath  isi  scopus
    26. Razgulin V A., Sazonova V S., “Hopf Bifurcation in Diffusive Model of Nonlinear Optical System With Matrix Fourier Filtering”, Commun. Nonlinear Sci. Numer. Simul., 77 (2019), 288–304  crossref  isi
    27. V. V. Liiko, A. L. Skubachevskii, “Silno ellipticheskie differentsialno-raznostnye uravneniya so smeshannymi kraevymi usloviyami v tsilindricheskoi oblasti”, Trudy Matematicheskogo instituta im. S.M. Nikolskogo RUDN, SMFN, 65, no. 4, Rossiiskii universitet druzhby narodov, M., 2019, 635–654  mathnet  crossref
    28. D. A. Neverova, “Gladkost obobschennykh reshenii vtoroi i tretei kraevykh zadach dlya silno ellipticheskikh differentsialno-raznostnykh uravnenii”, Trudy Matematicheskogo instituta im. S.M. Nikolskogo RUDN, SMFN, 65, no. 4, Rossiiskii universitet druzhby narodov, M., 2019, 655–671  mathnet  crossref
    29. Rossovskii L.E., Tovsultanov A.A., “Elliptic Functional Differential Equation With Affine Transformations”, J. Math. Anal. Appl., 480:2 (2019), 123403  crossref  isi
    30. Rossovskii L.E., Tovsultanov A.A., “on the Dirichlet Problem For An Elliptic Functional Differential Equation With Affine Transformations of the Argument”, Dokl. Math., 100:3 (2019), 551–553  crossref  isi
    31. V. V. Liiko, A. L. Skubachevskii, “Mixed Problems for Strongly Elliptic Differential-Difference Equations in a Cylinder”, Math. Notes, 107:5 (2020), 770–790  mathnet  crossref  crossref  isi  elib
    32. A. M. Selitskii, “On solvability of parabolic functional differential equations in Banach spaces (II)”, Eurasian Math. J., 11:2 (2020), 86–92  mathnet  crossref
    33. N. B. Zhuravlev, L. E. Rossovskii, “Spektralnyi radius parametricheskogo semeistva funktsionalnykh operatorov”, UMN, 75:5(455) (2020), 195–196  mathnet  crossref  mathscinet
    34. A. B. Muravnik, “Elliptic Differential-Difference Equations in the Half-Space”, Math. Notes, 108:5 (2020), 727–732  mathnet  crossref  crossref
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:725
    Full text:104
    References:83
    First page:96

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020