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Algebra i Analiz, 2003, Volume 15, Issue 5, Pages 1–108 (Mi aa817)  

This article is cited in 106 scientific papers (total in 106 papers)

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Periodic differential operators of second order. Threshold properties and averagings

M. Sh. Birman, T. A. Suslina

St. Petersburg State University, Faculty of Physics

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St. Petersburg Mathematical Journal, 2004, 15:5, 639–714

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Received: 25.06.2003

Citation: M. Sh. Birman, T. A. Suslina, “Periodic differential operators of second order. Threshold properties and averagings”, Algebra i Analiz, 15:5 (2003), 1–108; St. Petersburg Math. J., 15:5 (2004), 639–714

Citation in format AMSBIB
\by M.~Sh.~Birman, T.~A.~Suslina
\paper Periodic differential operators of second order. Threshold properties and averagings
\jour Algebra i Analiz
\yr 2003
\vol 15
\issue 5
\pages 1--108
\jour St. Petersburg Math. J.
\yr 2004
\vol 15
\issue 5
\pages 639--714

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    This publication is cited in the following articles:
    1. M. Sh. Birman, T. A. Suslina, “Homogenization of a multidimensional periodic elliptic operator in a neighbourhood of the edge of the internal gap”, J. Math. Sci. (N. Y.), 136:2 (2006), 3682–3690  mathnet  crossref  mathscinet  zmath  elib
    2. T. A. Suslina, “On the Homogenization of the Periodic Maxwell System”, Funct. Anal. Appl., 38:3 (2004), 234–237  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. T. A. Suslina, “On Homogenization of Periodic Parabolic Systems”, Funct. Anal. Appl., 38:4 (2004), 309–312  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. V. S. Buslaev, M. Z. Solomyak, D. R. Yafaev, “Mikhail Shlemovich Birman (on the Occasion of his 75th Birthday)”, St. Petersburg Math. J., 16:1 (2005), 1–8  mathnet  crossref  mathscinet  zmath
    5. T. A. Suslina, “On averaging of periodic elliptic operators in a strip domain”, St. Petersburg Math. J., 16:1 (2005), 237–257  mathnet  crossref  mathscinet  zmath
    6. V. V. Zhikov, “On gaps in the spectrum of some divergence elliptic operators with periodic coefficients”, St. Petersburg Math. J., 16:5 (2005), 773–790  mathnet  crossref  mathscinet  zmath
    7. T. A. Suslina, “Averaging of the stationary periodic Maxwell system”, St. Petersburg Math. J., 16:5 (2005), 863–922  mathnet  crossref  mathscinet  zmath
    8. Zhikov V. V., Pastukhova S. E., “On operator estimates for some problems in homogenization theory”, Russ. J. Math. Phys., 12:4 (2005), 515–524  mathscinet  zmath  isi  elib
    9. V. V. Zhikov, “On operator estimates in homogenization theory”, Dokl. Math., 72:1 (2005), 535–538  mathnet  mathscinet  zmath  isi  elib  elib
    10. V. V. Zhikov, “Spectral Method in Homogenization Theory”, Proc. Steklov Inst. Math., 250 (2005), 85–94  mathnet  mathscinet  zmath
    11. M. Sh. Birman, T. A. Suslina, “Threshold approximations for the resolvent of a factoried selfadjoint family with corrector”, St. Petersburg Math. J., 17:5 (2006), 745–762  mathnet  crossref  mathscinet  zmath
    12. R. G. Shterenberg, “On the structure of the lower spectral edge for a magnetic Schrödinger operator with small magnetic potential”, St. Petersburg Math. J., 17:5 (2006), 865–873  mathnet  crossref  mathscinet  zmath
    13. M. Sh. Birman, T. A. Suslina, “Averaging of periodic elliptic differential operators with the account of a corrector”, St. Petersburg Math. J., 17:6 (2006), 897–973  mathnet  crossref  mathscinet  zmath  elib
    14. Kamotski V., Matthies K., Smyshlyaev V. P., “Exponential homogenization of linear second order elliptic PDEs with periodic coefficients”, SIAM J. Math. Anal., 38:5 (2006), 1565–1587 (electronic)  crossref  mathscinet  isi  elib  scopus
    15. S. A. Nazarov, “Homogenization of elliptic systems with periodic coefficients: Weighted $L^p$ and $L^\infty$ estimates for asymptotic remainders”, St. Petersburg Math. J., 18:2 (2007), 269–304  mathnet  crossref  mathscinet  zmath  elib
    16. 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
    17. R. G. Shterenberg, “On homogenization of a periodic magnetic Schrödinger operator with degenerate lower edge of the spectrum”, J. Math. Sci. (N. Y.), 143:2 (2007), 3004–3009  mathnet  crossref  mathscinet  zmath  elib
    18. Pastukhova S.E., “Some estimates from homogenized elasticity problems”, Dokl. Math., 73:1 (2006), 102–106  mathnet  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    19. Borisov D.I., “Asymptotics of the spectrum of the Schrödinger operator perturbed by a rapidly oscillating periodic potential”, Dokl. Math., 73:1 (2006), 19–22  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    20. 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
    21. 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
    22. D. I. Borisov, “Asymptotics of the eigenvalues of elliptic systems with fast oscillating coefficients”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S35–S45  mathnet  crossref  elib
    23. Pastukhova S.E., Tikhomirov R.N., “Operator estimates in reiterated and locally periodic homogenization”, Dokl. Math., 76:1 (2007), 548–553  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    24. Kuchment P., Pinchover Y., “Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds”, Transactions of the American Mathematical Society, 359:12 (2007), 5777–5815  crossref  mathscinet  zmath  isi  scopus
    25. 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
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    27. 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
    28. 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
    29. 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
    30. 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
    31. 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
    32. Pastukhova S.E., Tikhomirov R.N., “Estimates of locally periodic and reiterated homogenization for parabolic equations”, Dokl. Math., 80:2 (2009), 674–678  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    33. Briet Ph., Kovarik H., Raikov G., Soccorsi E., “Eigenvalue Asymptotics in a Twisted Waveguide”, Communications in Partial Differential Equations, 34:8 (2009), 818–836  crossref  mathscinet  zmath  isi  scopus
    34. 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  mathscinet  zmath  isi
    35. 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
    36. Pastukhova S., “Estimates in homogenization of parabolic equations with locally periodic coefficients”, Asymptotic Analysis, 66:3–4 (2010), 207–228  mathscinet  zmath  isi  elib
    37. 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
    38. 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
    39. 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
    40. Suslina T., “Homogenization of a Periodic Parabolic Cauchy Problem in the Sobolev Space H-1(R-d)”, Mathematical Modelling of Natural Phenomena, 5:4 (2010), 390–447  crossref  mathscinet  zmath  isi  scopus
    41. Andrianov I.V., Awrejcewicz J., Danishevs'kyy V.V., Weichert D., “Wave Propagation in Periodic Composites: Higher-Order Asymptotic Analysis Versus Plane-Wave Expansions Method”, Journal of Computational and Nonlinear Dynamics, 6:1 (2011), 011015  crossref  mathscinet  isi  scopus
    42. 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
    43. 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
    44. 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
    45. M. A. Pakhnin, T. A. Suslina, “Homogenization of the Elliptic Dirichlet Problem: Error Estimates in the $(L_2\to H^1)$-Norm”, Funct. Anal. Appl., 46:2 (2012), 155–159  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    46. 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
    47. T. A. Suslina, “Operator Error Estimates in $L_2$ for Homogenization of an Elliptic Dirichlet Problem”, Funct. Anal. Appl., 46:3 (2012), 234–238  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    48. 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
    49. Kuchment P. Raich A., “Green's Function Asymptotics Near the Internal Edges of Spectra of Periodic Elliptic Operators. Spectral Edge Case”, Math. Nachr., 285:14-15 (2012), 1880–1894  crossref  mathscinet  zmath  isi  elib  scopus
    50. N. N. Senik, “Homogenization for a periodic elliptic operator in a strip with various boundary conditions”, St. Petersburg Math. J., 25:4 (2014), 647–697  mathnet  crossref  mathscinet  zmath  isi  elib
    51. 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
    52. 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
    53. Cardone G., Pastukhova S.E., Perugia C., “Estimates in Homogenization of Degenerate Elliptic Equations by Spectral Method”, Asymptotic Anal., 81:3-4 (2013), 189–209  crossref  mathscinet  zmath  isi  elib  scopus
    54. Suslina T.A., “Homogenization of the Dirichlet Problem for Elliptic Systems: l-2-Operator Error Estimates”, Mathematika, 59:2 (2013), 463–476  crossref  mathscinet  zmath  isi  elib  scopus
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    60. Fefferman Ch.L., Weinstein M.I., “Wave Packets in Honeycomb Structures and Two-Dimensional Dirac Equations”, Commun. Math. Phys., 326:1 (2014), 251–286  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    61. 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
    62. Duchene V. Vukicevic I. Weinstein M.I., “Homogenized Description of Defect Modes in Periodic Structures With Localized Defects”, Commun. Math. Sci., 13:3 (2015), 777–823  crossref  mathscinet  zmath  isi  elib  scopus
    63. S. E. Pastukhova, “The Neumann problem for elliptic equations with multiscale coefficients: operator estimates for homogenization”, Sb. Math., 207:3 (2016), 418–443  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    64. Korotyaev E. Saburova N., “Effective Masses For Laplacians on Periodic Graphs”, J. Math. Anal. Appl., 436:1 (2016), 104–130  crossref  mathscinet  zmath  isi  elib  scopus
    65. Cherednichenko K.D., Cooper S., “Resolvent Estimates For High-Contrast Elliptic Problems With Periodic Coefficients”, Arch. Ration. Mech. Anal., 219:3 (2016), 1061–1086  crossref  mathscinet  zmath  isi  elib  scopus
    66. 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
    67. S. E. Pastukhova, “Homogenization estimates of operator type for fourth order elliptic equations”, St. Petersburg Math. J., 28:2 (2017), 273–289  mathnet  crossref  mathscinet  isi  elib
    68. V. V. Zhikov, S. E. Pastukhova, “Operator estimates in homogenization theory”, Russian Math. Surveys, 71:3 (2016), 417–511  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    69. V. V. Zhikov, S. E. Pastukhova, “On the convergence of bloch eigenfunctions in homogenization problems”, Funct. Anal. Appl., 50:3 (2016), 204–218  mathnet  crossref  crossref  mathscinet  isi  elib
    70. T. A. Suslina, “Homogenization of Schrödinger-Type equations”, Funct. Anal. Appl., 50:3 (2016), 241–246  mathnet  crossref  crossref  mathscinet  isi  elib
    71. M. Dorodnyi, T. A. Suslina, “Homogenization of Hyperbolic Equations”, Funct. Anal. Appl., 50:4 (2016), 319–324  mathnet  crossref  crossref  mathscinet  isi  elib
    72. Xu Q., “Convergence Rates for General Elliptic Homogenization Problems in Lipschitz Domains”, SIAM J. Math. Anal., 48:6 (2016), 3742–3788  crossref  mathscinet  zmath  isi  scopus
    73. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
    74. Xu Q., “Uniform regularity estimates in homogenization theory of elliptic system with lower order terms”, J. Math. Anal. Appl., 438:2 (2016), 1066–1107  crossref  mathscinet  zmath  isi  elib  scopus
    75. 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
    76. Pastukhova S.E., “Estimates in homogenization of higher-order elliptic operators”, Appl. Anal., 95:7, SI (2016), 1449–1466  crossref  mathscinet  zmath  isi  elib  scopus
    77. 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
    78. 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
    79. Geng J., Shen Zh., “Convergence rates in parabolic homogenization with time-dependent periodic coefficients”, J. Funct. Anal., 272:5 (2017), 2092–2113  crossref  mathscinet  zmath  isi  scopus
    80. Maling B., Colquitt D.J., Craster R.V., “Dynamic homogenisation of Maxwell's equations with applications to photonic crystals and localised waveforms on gratings”, Wave Motion, 69 (2017), 35–49  crossref  mathscinet  isi  scopus
    81. 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
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    83. Yu. M. Meshkova, T. A. Suslina, “Homogenization of the Dirichlet problem for elliptic and parabolic systems with periodic coefficients”, Funct. Anal. Appl., 51:3 (2017), 230–235  mathnet  crossref  crossref  isi  elib
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    85. 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
    86. S. E. Pastukhova, R. N. Tikhomirov, “Operator-type estimates in homogenization of elliptic equations with lower terms”, St. Petersburg Math. J., 29:5 (2018), 841–861  mathnet  crossref  mathscinet  isi  elib
    87. 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
    88. Xu Q., “Convergence Rates and W-1,W-P Estimates in Homogenization Theory of Stokes Systems in Lipschitz Domains”, J. Differ. Equ., 263:1 (2017), 398–450  crossref  mathscinet  zmath  isi  elib  scopus
    89. 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
    90. Kha M., Kuchment P., Raich A., “Green'S Function Asymptotics Near the Internal Edges of Spectra of Periodic Elliptic Operators. Spectral Gap Interior”, J. Spectr. Theory, 7:4 (2017), 1171–1233  crossref  mathscinet  zmath  isi  scopus
    91. M. M. Sirazhudinov, “Operatornye otsenki usredneniya obobschennykh uravnenii Beltrami”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 7, 40–46  mathnet  crossref
    92. Cherednichenko K., Waurick M., “Resolvent Estimates in Homogenisation of Periodic Problems of Fractional Elasticity”, J. Differ. Equ., 264:6 (2018), 3811–3835  crossref  mathscinet  zmath  isi  scopus
    93. Chill R., ter Elst A.F.M., “Weak and Strong Approximation of Semigroups on Hilbert Spaces”, Integr. Equ. Oper. Theory, 90:1 (2018), UNSP 9  crossref  mathscinet  isi  scopus
    94. Suslina T.A., “Homogenization of the Neumann Problem For Higher Order Elliptic Equations With Periodic Coefficients”, Complex Var. Elliptic Equ., 63:7-8, SI (2018), 1185–1215  crossref  mathscinet  zmath  isi  scopus
    95. 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
    96. 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
    97. E. Korotyaev, N. Saburova, “Spektralnye otsenki dlya operatora Shredingera na periodicheskikh diskretnykh grafakh”, Algebra i analiz, 30:4 (2018), 61–106  mathnet
    98. K. S. Ryadovkin, “Asimptoticheskoe povedenie vetvyaschikhsya sluchainykh bluzhdanii na nekotorykh dvumernykh reshetkakh”, Veroyatnost i statistika. 27, Zap. nauchn. sem. POMI, 474, POMI, SPb., 2018, 213–221  mathnet
    99. Filonov N. Kachkovskiy I., “On the Structure of Band Edges of 2-Dimensional Periodic Elliptic Operators”, Acta Math., 221:1 (2018), 59–80  crossref  mathscinet  zmath  isi  scopus
    100. Khrabustovskyi A. Post O., “Operator Estimates For the Crushed Ice Problem”, Asymptotic Anal., 110:3-4 (2018), 137–161  crossref  isi
    101. T. A. Suslina, “Ob usrednenii statsionarnoi periodicheskoi sistemy Maksvella v ogranichennoi oblasti”, Funkts. analiz i ego pril., 53:1 (2019), 88–92  mathnet  crossref  elib
    102. 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
    103. M. V. Platonova, K. S. Ryadovkin, “Vetvyaschiesya sluchainye bluzhdaniya na $\mathbf{Z}^d$ s periodicheski raspolozhennymi istochnikami vetvleniya”, Teoriya veroyatn. i ee primen., 64:2 (2019), 283–307  mathnet  crossref  elib
    104. Yu. M. Meshkova, “Ob usrednenii periodicheskikh giperbolicheskikh sistem”, Matem. zametki, 105:6 (2019), 937–942  mathnet  crossref
    105. Lee-Thorp J.P., Weinstein M.I., Zhu Y., “Elliptic Operators With Honeycomb Symmetry: Dirac Points, Edge States and Applications to Photonic Graphene”, Arch. Ration. Mech. Anal., 232:1 (2019), 1–63  crossref  mathscinet  zmath  isi  scopus
    106. Cooper Sh., Waurick M., “Fibre Homogenisation”, J. Funct. Anal., 276:11 (2019), 3363–3405  crossref  mathscinet  zmath  isi  scopus
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