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Zhikov Vasilii Vasil'evich

Publications in Math-Net.Ru

  1. Homogenization and two-scale convergence in Sobolev space with oscillating exponent

    Algebra i Analiz, 30:2 (2018),  114–144
  2. Large time asymptotics of fundamental solution for the diffusion equation in periodic medium and its application to estimates in the theory of averaging

    CMFD, 63:2 (2017),  223–246
  3. On the convergence of bloch eigenfunctions in homogenization problems

    Funktsional. Anal. i Prilozhen., 50:3 (2016),  47–65
  4. Operator estimates in homogenization theory

    Uspekhi Mat. Nauk, 71:3(429) (2016),  27–122
  5. О плотности гладких функций в весовых соболевских пространствах с переменным показателем

    Algebra i Analiz, 27:3 (2015),  95–124
  6. On integral representation of $\Gamma$-limit functionals

    Fundam. Prikl. Mat., 19:4 (2014),  101–120
  7. Uniform convexity and variational convergence

    Tr. Mosk. Mat. Obs., 75:2 (2014),  245–276
  8. The $\Gamma$-convergence of oscillating integrands with nonstandard coercivity and growth conditions

    Mat. Sb., 205:4 (2014),  33–68
  9. Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent

    Mat. Sb., 205:3 (2014),  3–14
  10. Introduction to the theory of two-scale convergence

    Tr. Semim. im. I. G. Petrovskogo, 29 (2013),  281–332
  11. On the Navier–Stokes equations: Existence theorems and energy equalities

    Trudy Mat. Inst. Steklova, 278 (2012),  75–95
  12. Estimates of the Nash–Aronson type for degenerating parabolic equations

    CMFD, 39 (2011),  66–78
  13. Homogenization of Monotone Operators Under Conditions of Coercitivity and Growth of Variable Order

    Mat. Zametki, 90:1 (2011),  53–69
  14. Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent

    Tr. Semim. im. I. G. Petrovskogo, 28 (2011),  8–74
  15. On the Property of Higher Integrability for Parabolic Systems of Variable Order of Nonlinearity

    Mat. Zametki, 87:2 (2010),  179–200
  16. Lemmas on compensated compactness in elliptic and parabolic equations

    Trudy Mat. Inst. Steklova, 270 (2010),  110–137
  17. Existence theorems for solutions of parabolic equations with variable order of nonlinearity

    Trudy Mat. Inst. Steklova, 270 (2010),  21–32
  18. New Approach to the Solvability of Generalized Navier–Stokes Equations

    Funktsional. Anal. i Prilozhen., 43:3 (2009),  33–53
  19. On the Technique for Passing to the Limit in Nonlinear Elliptic Equations

    Funktsional. Anal. i Prilozhen., 43:2 (2009),  19–38
  20. On passage to the limit in nonlinear elliptic equations

    Dokl. Akad. Nauk, 420:3 (2008),  300–305
  21. Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent

    Mat. Sb., 199:12 (2008),  19–52
  22. Homogenization of degenerate elliptic equations

    Sibirsk. Mat. Zh., 49:1 (2008),  101–124
  23. Solvability of the Three-Dimensional Thermistor Problem

    Trudy Mat. Inst. Steklova, 261 (2008),  101–114
  24. On the Trotter–Kato Theorem in a Variable Space

    Funktsional. Anal. i Prilozhen., 41:4 (2007),  22–29
  25. Diffusion in an incompressible random flow. Estimates of Nash-Aronson type for transition probabilities, and the central limit theorem

    Dokl. Akad. Nauk, 407:4 (2006),  439–442
  26. Homogenization of random singular structures and random measures

    Izv. RAN. Ser. Mat., 70:1 (2006),  23–74
  27. Estimates of the Nash–Aronson type for the diffusion equation with non-symmetric matrix and their application to homogenization

    Mat. Sb., 197:12 (2006),  65–94
  28. Derivation of the limit equations of elasticity theory on thin nets

    Tr. Semim. im. I. G. Petrovskogo, 25 (2006),  55–97
  29. Homogenized Tensor on Networks

    Trudy Mat. Inst. Steklova, 250 (2005),  105–111
  30. Spectral Method in Homogenization Theory

    Trudy Mat. Inst. Steklova, 250 (2005),  95–104
  31. On gaps in the spectrum of some divergence elliptic operators with periodic coefficients

    Algebra i Analiz, 16:5 (2004),  34–58
  32. Remarks on the Uniqueness of a Solution of the Dirichlet Problem for Second-Order Elliptic Equations with Lower-Order Terms

    Funktsional. Anal. i Prilozhen., 38:3 (2004),  15–28
  33. On density of smooth functions in Sobolev–Orlich spaces

    Zap. Nauchn. Sem. POMI, 310 (2004),  67–81
  34. Homogenization for elasticity problems on periodic networks of critical thickness

    Mat. Sb., 194:5 (2003),  61–96
  35. Homogenization of elasticity problems on singular structures

    Izv. RAN. Ser. Mat., 66:2 (2002),  81–148
  36. To the Problem of Passage to the Limit in Divergent Nonuniformly Elliptic Equations

    Funktsional. Anal. i Prilozhen., 35:1 (2001),  23–39
  37. On an extension of the method of two-scale convergence and its applications

    Mat. Sb., 191:7 (2000),  31–72
  38. On the Homogenization Technique for Variational Problems

    Funktsional. Anal. i Prilozhen., 33:1 (1999),  14–29
  39. The leading term of the spectral asymptotics for the Kohn–Laplace operator in a bounded domain

    Mat. Zametki, 64:4 (1998),  493–505
  40. Weighted Sobolev spaces

    Mat. Sb., 189:8 (1998),  27–58
  41. Meyer-type estimates for solving the nonlinear Stokes system

    Differ. Uravn., 33:1 (1997),  107–114
  42. Diffusion in an Incompressible Random Flow

    Funktsional. Anal. i Prilozhen., 31:3 (1997),  10–22
  43. Homogenization of non-linear second-order elliptic equations in perforated domains

    Izv. RAN. Ser. Mat., 61:1 (1997),  69–88
  44. Connectedness and homogenization. Examples of fractal conductivity

    Mat. Sb., 187:8 (1996),  3–40
  45. On the averaging of nonlinear variational problems in punctured domains

    Dokl. Akad. Nauk, 345:2 (1995),  156–160
  46. On the Lavrent'ev effect

    Dokl. Akad. Nauk, 345:1 (1995),  10–14
  47. On the averaging of the system of Stokes equations in a punctured domain

    Dokl. Akad. Nauk, 334:2 (1994),  144–147
  48. Asymptotic problems related to a second-order parabolic equation in nondivergence form with randomly homogeneous coefficients

    Differ. Uravn., 29:5 (1993),  859–869
  49. The limit load and homogenization

    Izv. RAN. Ser. Mat., 57:5 (1993),  15–43
  50. Averaging in perforated random domains of general type

    Mat. Zametki, 53:1 (1993),  41–58
  51. Threshold of conductivity for a random cubic structure

    Mat. Zametki, 52:6 (1992),  15–24
  52. On passage to the limit in nonlinear variational problems

    Mat. Sb., 183:8 (1992),  47–84
  53. The Lavrent'ev effect and averaging of nonlinear variational problems

    Differ. Uravn., 27:1 (1991),  42–50
  54. Estimates for the averaged matrix and the averaged tensor

    Uspekhi Mat. Nauk, 46:3(279) (1991),  49–109
  55. Problems of the continuation of functions in connection with averaging theory

    Differ. Uravn., 26:1 (1990),  39–50
  56. Asymptotic problems connected with the heat equation in perforated domains

    Mat. Sb., 181:10 (1990),  1283–1305
  57. Spectral approach to asymptotic diffusion problems

    Differ. Uravn., 25:1 (1989),  44–50
  58. Effective conductivity of random homogeneous sets

    Mat. Zametki, 45:4 (1989),  34–45
  59. Remarks on the problem of residual diffusion

    Uspekhi Mat. Nauk, 44:6(270) (1989),  155–156
  60. Estimates for the trace of an averaged tensor

    Dokl. Akad. Nauk SSSR, 299:4 (1988),  796–800
  61. Averaging of a system of Beltrami equations

    Differ. Uravn., 24:1 (1988),  64–73
  62. Averaging of functionals of the calculus of variations and elasticity theory

    Izv. Akad. Nauk SSSR Ser. Mat., 50:4 (1986),  675–710
  63. Estimates for the trace of the averaged matrix

    Mat. Zametki, 40:2 (1986),  226–237
  64. Stabilization of the solution of the Cauchy problem for parabolic equations

    Mat. Zametki, 37:6 (1985),  834–850
  65. Questions of convergence, duality, and averaging for functionals of the calculus of variations

    Izv. Akad. Nauk SSSR Ser. Mat., 47:5 (1983),  961–998
  66. Asymptotic behavior and stabilization of solutions of a second-order parabolic equation with lowest terms

    Tr. Mosk. Mat. Obs., 46 (1983),  69–98
  67. Averaging of singularly perturbed elliptic operators

    Mat. Zametki, 33:4 (1983),  571–582
  68. $G$-convergence of elliptic operators

    Mat. Zametki, 33:3 (1983),  345–356
  69. Questions of convergence, duality, and averaging for a certain class of functionals in variational calculus

    Dokl. Akad. Nauk SSSR, 267:3 (1982),  524–528
  70. Averaging of parabolic operators

    Tr. Mosk. Mat. Obs., 45 (1982),  182–236
  71. Averaging of parabolic operators with almost periodic coefficients

    Mat. Sb. (N.S.), 117(159):1 (1982),  69–85
  72. Averaging of a system of elasticity theory with almost periodic coefficients

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1982, no. 6,  62–70
  73. Theorems on the averaging of parabolic operators

    Dokl. Akad. Nauk SSSR, 260:3 (1981),  521–525
  74. On $G$-compactness of a class of nondivergence elliptic operators of second order

    Izv. Akad. Nauk SSSR Ser. Mat., 45:4 (1981),  718–733
  75. $G$-convergence of parabolic operators

    Uspekhi Mat. Nauk, 36:1(217) (1981),  11–58
  76. The averaging of nondivergence second order elliptic and parabolic operators and the stabilization of solutions of the Cauchy problem

    Mat. Sb. (N.S.), 116(158):2(10) (1981),  166–186
  77. Averaging and $G$-convergence of differential operators

    Uspekhi Mat. Nauk, 34:5(209) (1979),  65–133
  78. A point stabilization criterion for second order parabolic equations with almost periodic coefficients

    Mat. Sb. (N.S.), 110(152):2(10) (1979),  304–318
  79. Proof of the Favard theorem on the existence of almost-periodic solution for an arbitrary Banach space

    Mat. Zametki, 23:1 (1978),  121–126
  80. Favard theory

    Uspekhi Mat. Nauk, 32:2(194) (1977),  123–171
  81. On the stabilization of solutions of parabolic equations

    Mat. Sb. (N.S.), 104(146):4(12) (1977),  597–616
  82. Some admissibility and dichotomy questions. The averaging principle

    Izv. Akad. Nauk SSSR Ser. Mat., 40:6 (1976),  1380–1408
  83. The invertibility of the operator $d/dt+A(t)$ in the space of bounded functions

    Mat. Zametki, 19:1 (1976),  99–104
  84. Solvability of linear equations in the Besicovitch and Bohr classes of almost periodic functions

    Mat. Zametki, 18:4 (1975),  553–560
  85. Some new results in abstract Favar theory

    Mat. Zametki, 17:1 (1975),  33–40
  86. The averaging principle for parabolic equations with variable principal term

    Dokl. Akad. Nauk SSSR, 208:1 (1973),  32–35
  87. Monotonicity in the theory of almost periodic solutions of nonlinear operator equations

    Mat. Sb. (N.S.), 90(132):2 (1973),  214–228
  88. On the theory of admissibility of pairs of function spaces

    Dokl. Akad. Nauk SSSR, 205:6 (1972),  1281–1283
  89. The stability and instability of Levinson's center

    Differ. Uravn., 8:12 (1972),  2167–2170
  90. Certain functional methods in the theory of almost periodic solutions. I

    Differ. Uravn., 7:2 (1971),  215–225
  91. Remarks on compactness conditions related to the work of M. I. Kadets on integration of abstract almost-periodic functions

    Funktsional. Anal. i Prilozhen., 5:1 (1971),  30–36
  92. The existence of Levitan almost-periodic solutions of linear systems (second complement to Favard's classical theory)

    Mat. Zametki, 9:4 (1971),  409–414
  93. Almost periodic solutions of linear and nonlinear equations in a Banach space

    Dokl. Akad. Nauk SSSR, 195:2 (1970),  278–281
  94. Addition to the classical theory of Favard

    Mat. Zametki, 7:2 (1970),  239–246
  95. On a problem of Bochner and von Neumann

    Mat. Zametki, 3:5 (1968),  529–538
  96. On inverse Sturm–Liouville problems on a finite segment

    Izv. Akad. Nauk SSSR Ser. Mat., 31:5 (1967),  965–976
  97. Conditions for discreteness and finiteness of the negative spectrum of Schrödinger's operator equation

    Mat. Zametki, 2:5 (1967),  531–538
  98. On the question of harmonic analysis of bounded solutions of operator equations

    Dokl. Akad. Nauk SSSR, 169:6 (1966),  1254–1257
  99. Almost periodic solutions of differential equations in Hilbert space

    Dokl. Akad. Nauk SSSR, 165:6 (1965),  1227–1230
  100. Abstract equations with almost-periodic coefficients

    Dokl. Akad. Nauk SSSR, 163:3 (1965),  555–558

  101. To the memory of Boris Moiseevich Levitan (on the 100th anniversary of his birth)

    Uspekhi Mat. Nauk, 71:3(429) (2016),  207–209
  102. In memory of Boris Moiseevich Levitan (1914–2004)

    Tr. Mosk. Mat. Obs., 75:2 (2014),  105–106
  103. Vladimir Alexandrovich Kondratiev. July 2, 1935 – March 11, 2010

    CMFD, 39 (2011),  5–10
  104. Olga Arsenjevna Oleinik

    Tr. Semim. im. I. G. Petrovskogo, 28 (2011),  5–7
  105. Ol'ga Arsen'evna Oleinik (obituary)

    Uspekhi Mat. Nauk, 58:1(349) (2003),  165–174
  106. Sergei Mikhailovich Kozlov (obituary)

    Uspekhi Mat. Nauk, 51:4(310) (1996),  145–146

© Steklov Math. Inst. of RAS, 2025