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Algebra i Analiz, 2005, Volume 17, Issue 6, Pages 1–104 (Mi aa714)  

This article is cited in 50 scientific papers (total in 50 papers)

Expository Surveys

Averaging of periodic elliptic differential operators with the account of a corrector

M. Sh. Birman, T. A. Suslina

St. Petersburg State University, Faculty of Physics

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St. Petersburg Mathematical Journal, 2006, 17:6, 897–973

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Received: 17.10.2005

Citation: M. Sh. Birman, T. A. Suslina, “Averaging of periodic elliptic differential operators with the account of a corrector”, Algebra i Analiz, 17:6 (2005), 1–104; St. Petersburg Math. J., 17:6 (2006), 897–973

Citation in format AMSBIB
\Bibitem{BirSus05}
\by M.~Sh.~Birman, T.~A.~Suslina
\paper Averaging of periodic elliptic differential operators with the account of a~corrector
\jour Algebra i Analiz
\yr 2005
\vol 17
\issue 6
\pages 1--104
\mathnet{http://mi.mathnet.ru/aa714}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2202045}
\zmath{https://zbmath.org/?q=an:1175.35007}
\elib{http://elibrary.ru/item.asp?id=9188322}
\transl
\jour St. Petersburg Math. J.
\yr 2006
\vol 17
\issue 6
\pages 897--973
\crossref{https://doi.org/10.1090/S1061-0022-06-00935-6}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Sh. Birman, T. A. Suslina, “Homogenization with corrector for periodic differential operators. Approximation of solutions in the Sobolev class $H^1(\mathbb R^d)$”, St. Petersburg Math. J., 18:6 (2007), 857–955  mathnet  crossref  mathscinet  zmath
    2. M. Sh. Birman, T. A. Suslina, “Homogenization of the Stationary Periodic Maxwell System in the Case of Constant Permeability”, Funct. Anal. Appl., 41:2 (2007), 81–98  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. T. A. Suslina, “Homogenization with corrector for a stationary periodic Maxwell system”, St. Petersburg Math. J., 19:3 (2008), 455–494  mathnet  crossref  mathscinet  zmath  isi
    4. D. I. Borisov, “Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients”, St. Petersburg Math. J., 20:2 (2009), 175–191  mathnet  crossref  mathscinet  zmath  isi
    5. V. V. Zhikov, S. E. Pastukhova, “Homogenization of degenerate elliptic equations”, Siberian Math. J., 49:1 (2008), 80–101  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    6. S. E. Pastukhova, “Operator Estimates in Nonlinear Problems of Reiterated Homogenization”, Proc. Steklov Inst. Math., 261 (2008), 214–228  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    7. M. Sh. Birman, T. A. Suslina, “Operator error estimates in the homogenization problem for nonstationary periodic equations”, St. Petersburg Math. J., 20:6 (2009), 873–928  mathnet  crossref  mathscinet  zmath  isi
    8. E. S. Vasilevskaya, “Homogenization with a corrector for a parabolic Cauchy problem with periodic coefficients”, St. Petersburg Math. J., 21:1 (2010), 1–41  mathnet  crossref  mathscinet  zmath  isi
    9. G. Cardone, A. Corbo Esposito, S. A. Nazarov, “Homogenization of the mixed boundary value problem for a formally self-adjoint system in a periodically perforated domain”, St. Petersburg Math. J., 21:4 (2010), 601–634  mathnet  crossref  mathscinet  zmath  isi
    10. Borisov D., Cardone G., “Homogenization of the planar waveguide with frequently alternating boundary conditions”, J. Phys. A, 42:36 (2009), 365205, 21 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    11. Birman M.S., Suslina T.A., “Homogenization of Periodic Differential Operators as a Spectral Threshold Effect”, New Trends in Mathematical Physics, 2009, 667–683  crossref  zmath  isi
    12. T. A. Suslina, “Homogenization in Sobolev class $H^1(\mathbb R^d)$ for periodic elliptic second order differential operators including first order terms”, St. Petersburg Math. J., 22:1 (2011), 81–162  mathnet  crossref  mathscinet  zmath  isi
    13. N. A. Veniaminov, “Homogenization of periodic differential operators of high order”, St. Petersburg Math. J., 22:5 (2011), 751–775  mathnet  crossref  mathscinet  zmath  isi
    14. V. S. Buslaev, A. A. Pozharskii, “Homogenization in the Scattering Problem”, Funct. Anal. Appl., 44:4 (2010), 243–252  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. T. A. Suslina, “Homogenization of the Parabolic Cauchy Problem in the Sobolev Class $H^1(\mathbb{R}^d)$”, Funct. Anal. Appl., 44:4 (2010), 318–322  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. Suslina T., “Homogenization of a periodic parabolic Cauchy problem in the Sobolev space $H^1(\mathbb R^d)$”, Mathematical Modelling of Natural Phenomena, 5:4 (2010), 390–447  crossref  mathscinet  zmath  isi  scopus
    17. Borisov D., Bunoiu R., Cardone G., “On a Waveguide with Frequently Alternating Boundary Conditions: Homogenized Neumann Condition”, Ann Henri Poincaré, 11:8 (2010), 1591–1627  crossref  mathscinet  zmath  adsnasa  isi  scopus
    18. M. Z. Solomyak, T. A. Suslina, D. R. Yafaev, “On the mathematical works of M. Sh. Birman”, St. Petersburg Math. J., 23:1 (2012), 1–38  mathnet  crossref  mathscinet  zmath  isi  elib
    19. E. S. Vasilevskaya, T. A. Suslina, “Threshold approximations of a factorized selfadjoint operator family with the first and the second correctors taken into account”, St. Petersburg Math. J., 23:2 (2012), 275–308  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    20. Bunoiu R., Cardone G., Suslina T., “Spectral approach to homogenization of an elliptic operator periodic in some directions”, Math Methods Appl Sci, 34:9 (2011), 1075–1096  crossref  mathscinet  zmath  isi  elib  scopus
    21. Borisov D., Cardone G., “Planar waveguide with “twisted” boundary conditions: Small width”, J Math Phys, 53:2 (2012), 023503  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    22. E. S. Vasilevskaya, T. A. Suslina, “Homogenization of parabolic and elliptic periodic operators in $L_2(\mathbb R^d)$ with the first and second correctors taken into account”, St. Petersburg Math. J., 24:2 (2013), 185–261  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    23. M. A. Pakhnin, T. A. Suslina, “Operator error estimates for homogenization of the elliptic Dirichlet problem in a bounded domain”, St. Petersburg Math. J., 24:6 (2013), 949–976  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    24. S. E. Pastukhova, “Approximations of the operator exponential in a periodic diffusion problem with drift”, Sb. Math., 204:2 (2013), 280–306  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    25. S. E. Pastukhova, “Approximations of the Resolvent for a Non–Self-Adjoint Diffusion Operator with Rapidly Oscillating Coefficients”, Math. Notes, 94:1 (2013), 127–145  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    26. T. A. Suslina, “Approximation of the resolvent of a twoparametric quadratic operator pencil near the bottom of the spectrum”, St. Petersburg Math. J., 25:5 (2014), 869–891  mathnet  crossref  mathscinet  zmath  isi  elib
    27. Yu. M. Meshkova, “Homogenization of the Cauchy problem for parabolic systems with periodic coefficients”, St. Petersburg Math. J., 25:6 (2014), 981–1019  mathnet  crossref  mathscinet  zmath  isi  elib
    28. T. F. Sharapov, “On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition”, Sb. Math., 205:10 (2014), 1492–1527  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    29. T. A. Suslina, “Homogenization of elliptic systems with periodic coefficients: operator error estimates in $L_2(\mathbb R^d)$ with corrector taken into account”, St. Petersburg Math. J., 26:4 (2015), 643–693  mathnet  crossref  mathscinet  isi  elib  elib
    30. T. A. Suslina, “Homogenization of elliptic operators with periodic coefficients depending on the spectral parameter”, St. Petersburg Math. J., 27:4 (2016), 651–708  mathnet  crossref  mathscinet  isi  elib
    31. N. N. Senik, “On Homogenization for Non-Self-Adjoint Periodic Elliptic Operators on an Infinite Cylinder”, Funct. Anal. Appl., 50:1 (2016), 71–75  mathnet  crossref  crossref  mathscinet  isi  elib
    32. A. A. Kukushkin, T. A. Suslina, “Homogenization of high order elliptic operators with periodic coefficients”, St. Petersburg Math. J., 28:1 (2017), 65–108  mathnet  crossref  mathscinet  isi  elib
    33. T. A. Suslina, “Homogenization of Schrödinger-Type equations”, Funct. Anal. Appl., 50:3 (2016), 241–246  mathnet  crossref  crossref  mathscinet  isi  elib
    34. M. Dorodnyi, T. A. Suslina, “Homogenization of Hyperbolic Equations”, Funct. Anal. Appl., 50:4 (2016), 319–324  mathnet  crossref  crossref  mathscinet  isi  elib
    35. Borisov D., Cardone G., Durante T., “Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve”, Proc. R. Soc. Edinb. Sect. A-Math., 146:6 (2016), 1115–1158  crossref  mathscinet  zmath  isi  elib  scopus
    36. Meshkova Yu.M. Suslina T.A., “Two-parametric error estimates in homogenization of second-order elliptic systems in ^{ d }”, Appl. Anal., 95:7, SI (2016), 1413–1448  crossref  mathscinet  zmath  isi  elib  scopus
    37. Meshkova Yu.M. Suslina T.A., “Homogenization of initial boundary value problems for parabolic systems with periodic coefficients”, Appl. Anal., 95:8 (2016), 1736–1775  crossref  mathscinet  zmath  isi  elib  scopus
    38. N. N. Senik, “On homogenization for non-self-adjoint locally periodic elliptic operators”, Funct. Anal. Appl., 51:2 (2017), 152–156  mathnet  crossref  crossref  isi  elib
    39. Cherednichenko K.D., Kiselev A.V., “Norm-Resolvent Convergence of One-Dimensional High-Contrast Periodic Problems to a Kronig–Penney Dipole-Type Model”, Commun. Math. Phys., 349:2 (2017), 441–480  crossref  mathscinet  zmath  isi  elib  scopus
    40. Suslina T., “Spectral approach to homogenization of nonstationary Schrödinger-type equations”, J. Math. Anal. Appl., 446:2 (2017), 1466–1523  crossref  mathscinet  zmath  isi  elib  scopus
    41. T. A. Suslina, “Homogenization of the Dirichlet problem for higher-order elliptic equations with periodic coefficients”, St. Petersburg Math. J., 29:2 (2018), 325–362  mathnet  crossref  isi  elib
    42. M. Dorodnyi, T. A. Suslina, “Homogenization of a Nonstationary Model Equation of Electrodynamics”, Math. Notes, 102:5 (2017), 645–663  mathnet  crossref  crossref  mathscinet  isi  elib
    43. Yu. M. Meshkova, T. A. Suslina, “Usrednenie pervoi nachalno-kraevoi zadachi dlya parabolicheskikh sistem: operatornye otsenki pogreshnosti”, Algebra i analiz, 29:6 (2017), 99–158  mathnet  elib
    44. Bellieud M., “Homogenization of Stratified Elastic Composites With High Contrast”, SIAM J. Math. Anal., 49:4 (2017), 2615–2665  crossref  mathscinet  zmath  isi  scopus
    45. Cardone G., “Waveguides With Fast Oscillating Boundary”, Nanosyst.-Phys. Chem. Math., 8:2 (2017), 160–165  crossref  mathscinet  isi
    46. Senik N.N., “Homogenization For Non-Self-Adjoint Periodic Elliptic Operators on An Infinite Cylinder”, SIAM J. Math. Anal., 49:2 (2017), 874–898  crossref  mathscinet  zmath  isi  scopus
    47. Dorodnyi M.A., Suslina T.A., “Spectral Approach to Homogenization of Hyperbolic Equations With Periodic Coefficients”, J. Differ. Equ., 264:12 (2018), 7463–7522  crossref  mathscinet  zmath  isi
    48. Suslina T.A., “Spectral Approach to Homogenization of Elliptic Operators in a Perforated Space”, Rev. Math. Phys., 30:8, SI (2018), 1840016  crossref  mathscinet  isi  scopus
    49. T. A. Suslina, “Usrednenie statsionarnoi periodicheskoi sistemy Maksvella v ogranichennoi oblasti v sluchae postoyannoi magnitnoi pronitsaemosti”, Algebra i analiz, 30:3 (2018), 169–209  mathnet  elib
    50. Suslina T.A., “Homogenization of Higher-Order Parabolic Systems in a Bounded Domain”, Appl. Anal., 98:1-2, SI (2019), 3–31  crossref  mathscinet  zmath  isi  scopus
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