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Zhikov, Vasilii Vasil'evich
(1940–2017)

Statistics Math-Net.Ru
Total publications: 99
Scientific articles: 93
Presentations: 4

Number of views:
This page:10369
Abstract pages:37202
Full texts:11241
References:2604
Professor
Doctor of physico-mathematical sciences (1975)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 14.08.1940
Keywords: almost-periodic functions, elliptic and parabolic equations, homogenization, Lavrentiev phenomenon, Sobolev spaces, singular structures, nonstandard growth conditions, relaxation functional.

Subject:

Almost-periodic functions and solutions of differential equations, quality properties of equations in Banach spaces, spectral theory of differential operators, stabilization of solutions of parabolic equations. Homogenization of differential operators and variational functionals. Lavrentiev phenomenon. Variational problem for lagrangians with non-standard grows conditions. The concept of two-scale convergence associated with a fixed periodic Borel measure is introduced. In the case when our measure is Lebegue measure on the torus convergence in the sense of Nguetseng-Allaire is obtained. An application of two-scale convergence to the homogenization of some problems in the theory of porous media (the double-porosity model) is presented. A mathamatical notion of "softly or weakly coupled parallel flows" is worked out. A homogenized operator is constructed, and the convergence result itself is interpreted as a "strong two-scale resolvent convergence". Problems concerning the behaviour of the spectrum under homogenization are touched upon in this connection. We presented a Homogenization Theory on periodic networks, junctions and, more generally, Multi-dimensional Structures. We has shown that the Homogenized Problem has a non-classical character in most cases. This important fact is a distinctive feature of Elasticity Problems, in contrast to scalar Problems. A weighted Sobolev space is constructed in which smooth functions are not dense, and their closure is of codimension one. With the help of this weighted space, counterexamples to natural hypotheses on the passage to the limit in non-uniformly-elliptic equations and on the structure of the limit equation are constructed. We introduced a new class of weight functions (partially Muckenhoupt weights"). For the corresponding elliptic equation we proved the Holder continuity. At the same time the Harnack inequality, weight Sobolev inequality and double-condition fail. In particulary, the old problem by Fabes, Birolli, Serapioni is solved.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1963 (department of theory of functions and functional analysis). Ph. D. thesis was defended in 1970. D. Sci. thesis was defended in 1975. Since 1978 I have led the reseach seminar at VGPU on Partial differential equations. Since 2000 I have led the reseach seminar at MSU on Homogenization.

   
Main publications:
  1. Levitan B. M., Zhikov V. V., Pochti-periodicheskie funktsii i differentsialnye uravneniya, Izd. MGU, M., 1978  mathscinet  zmath
  2. Zhikov V. V., Kozlov S. M., Oleinik O. A., Usrednenie differentsialnykh operatorov, Nauka, M., 1993  mathscinet  zmath
  3. Jikov V. V., Kozlov S. M., Oleinik O. A., Homogenization of differential operators and integral functionals, Springer-Verlag, Berlin, 1994  mathscinet
  4. Zhikov V. V., “Svyaznost i usrednenie. Primery fraktalnoi provodimosti”, Matem. sb., 187:8 (1996), 3–40  mathnet  mathscinet  zmath
  5. Zhikov V. V., “Usrednenie zadach teorii uprugosti na singulyarnykh strukturakh”, Izvestiya RAN, ser. matem., 66:2 (2002), 81–148  mathnet  mathscinet  zmath

http://www.mathnet.ru/eng/person8458
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/190584

Publications in Math-Net.Ru
2018
1. V. V. Zhikov, S. E. Pastukhova, “Homogenization and two-scale convergence in Sobolev space with oscillating exponent”, Algebra i Analiz, 30:2 (2018),  114–144  mathnet  elib
2017
2. V. V. Zhikov, S. E. Pastukhova, “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  mathnet  mathscinet
2016
3. V. V. Zhikov, S. E. Pastukhova, “On the convergence of bloch eigenfunctions in homogenization problems”, Funktsional. Anal. i Prilozhen., 50:3 (2016),  47–65  mathnet  mathscinet  elib; Funct. Anal. Appl., 50:3 (2016), 204–218  isi  scopus
4. V. V. Zhikov, S. E. Pastukhova, “Operator estimates in homogenization theory”, Uspekhi Mat. Nauk, 71:3(429) (2016),  27–122  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 71:3 (2016), 417–511  isi  scopus
2015
5. V. V. Zhikov, M. D. Surnachev, “О плотности гладких функций в весовых соболевских пространствах с переменным показателем”, Algebra i Analiz, 27:3 (2015),  95–124  mathnet  mathscinet  elib; St. Petersburg Math. J., 27:3 (2016), 415–436  isi  scopus
2014
6. V. V. Zhikov, S. E. Pastukhova, “On integral representation of $\Gamma$-limit functionals”, Fundam. Prikl. Mat., 19:4 (2014),  101–120  mathnet  mathscinet; J. Math. Sci., 217:6 (2016), 736–750
7. V. V. Zhikov, S. E. Pastukhova, “Uniform convexity and variational convergence”, Tr. Mosk. Mat. Obs., 75:2 (2014),  245–276  mathnet  elib; Trans. Moscow Math. Soc., 75 (2014), 205–231  scopus
8. V. V. Zhikov, S. E. Pastukhova, “The $\Gamma$-convergence of oscillating integrands with nonstandard coercivity and growth conditions”, Mat. Sb., 205:4 (2014),  33–68  mathnet  mathscinet  zmath  elib; Sb. Math., 205:4 (2014), 488–521  isi  scopus
9. Yu. A. Alkhutov, V. V. Zhikov, “Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent”, Mat. Sb., 205:3 (2014),  3–14  mathnet  mathscinet  zmath  elib; Sb. Math., 205:3 (2014), 307–318  isi  scopus
2013
10. V. V. Zhikov, G. A. Yosifian, “Introduction to the theory of two-scale convergence”, Tr. Semim. im. I. G. Petrovskogo, 29 (2013),  281–332  mathnet  elib; J. Math. Sci. (N. Y.), 197:3 (2014), 325–357  scopus
2012
11. V. V. Zhikov, S. E. Pastukhova, “On the Navier–Stokes equations: Existence theorems and energy equalities”, Tr. Mat. Inst. Steklova, 278 (2012),  75–95  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 278 (2012), 67–87  isi  elib  scopus
2011
12. V. V. Zhikov, “Estimates of the Nash–Aronson type for degenerating parabolic equations”, CMFD, 39 (2011),  66–78  mathnet  mathscinet; Journal of Mathematical Sciences, 190:1 (2013), 66–79  scopus
13. V. V. Zhikov, S. E. Pastukhova, “Homogenization of Monotone Operators Under Conditions of Coercitivity and Growth of Variable Order”, Mat. Zametki, 90:1 (2011),  53–69  mathnet  mathscinet; Math. Notes, 90:1 (2011), 48–63  isi  scopus
14. Yu. A. Alkhutov, V. V. Zhikov, “Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent”, Tr. Semim. im. I. G. Petrovskogo, 28 (2011),  8–74  mathnet  zmath  elib; J. Math. Sci. (N. Y.), 179:3 (2011), 347–389  scopus
2010
15. V. V. Zhikov, S. E. Pastukhova, “On the Property of Higher Integrability for Parabolic Systems of Variable Order of Nonlinearity”, Mat. Zametki, 87:2 (2010),  179–200  mathnet  mathscinet  zmath; Math. Notes, 87:2 (2010), 169–188  isi  scopus
16. V. V. Zhikov, S. E. Pastukhova, “Lemmas on compensated compactness in elliptic and parabolic equations”, Tr. Mat. Inst. Steklova, 270 (2010),  110–137  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 270 (2010), 104–131  isi  scopus
17. Yu. A. Alkhutov, V. V. Zhikov, “Existence theorems for solutions of parabolic equations with variable order of nonlinearity”, Tr. Mat. Inst. Steklova, 270 (2010),  21–32  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 270 (2010), 15–26  isi  scopus
2009
18. V. V. Zhikov, “New Approach to the Solvability of Generalized Navier–Stokes Equations”, Funktsional. Anal. i Prilozhen., 43:3 (2009),  33–53  mathnet  mathscinet  zmath; Funct. Anal. Appl., 43:3 (2009), 190–207  isi  scopus
19. V. V. Zhikov, “On the Technique for Passing to the Limit in Nonlinear Elliptic Equations”, Funktsional. Anal. i Prilozhen., 43:2 (2009),  19–38  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 43:2 (2009), 96–112  isi  scopus
2008
20. V. V. Zhikov, “On passage to the limit in nonlinear elliptic equations”, Dokl. Akad. Nauk, 420:3 (2008),  300–305  mathnet  mathscinet; Dokl. Math., 77:3 (2008), 383–387  isi  scopus
21. V. V. Zhikov, S. E. Pastukhova, “Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent”, Mat. Sb., 199:12 (2008),  19–52  mathnet  mathscinet  zmath  elib; Sb. Math., 199:12 (2008), 1751–1782  isi  elib  scopus
22. V. V. Zhikov, S. E. Pastukhova, “Homogenization of degenerate elliptic equations”, Sibirsk. Mat. Zh., 49:1 (2008),  101–124  mathnet  mathscinet  zmath  elib; Siberian Math. J., 49:1 (2008), 80–101  isi  elib  scopus
23. V. V. Zhikov, “Solvability of the Three-Dimensional Thermistor Problem”, Tr. Mat. Inst. Steklova, 261 (2008),  101–114  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 261 (2008), 98–111  isi  elib  scopus
2007
24. V. V. Zhikov, S. E. Pastukhova, “On the Trotter–Kato Theorem in a Variable Space”, Funktsional. Anal. i Prilozhen., 41:4 (2007),  22–29  mathnet  mathscinet  zmath; Funct. Anal. Appl., 41:4 (2007), 264–270  isi  scopus
2006
25. V. V. Zhikov, “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  mathnet  mathscinet
26. V. V. Zhikov, A. L. Piatnitski, “Homogenization of random singular structures and random measures”, Izv. RAN. Ser. Mat., 70:1 (2006),  23–74  mathnet  mathscinet  zmath  elib; Izv. Math., 70:1 (2006), 19–67  isi  elib  scopus
27. V. V. Zhikov, “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  mathnet  mathscinet  zmath  elib; Sb. Math., 197:12 (2006), 1775–1804  isi  scopus
28. V. V. Zhikov, S. E. Pastukhova, “Derivation of the limit equations of elasticity theory on thin nets”, Tr. Semim. im. I. G. Petrovskogo, 25 (2006),  55–97  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 135:1 (2006), 2637–2665  scopus
2005
29. V. V. Zhikov, S. E. Pastukhova, “Homogenized Tensor on Networks”, Tr. Mat. Inst. Steklova, 250 (2005),  105–111  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 250 (2005), 95–101
30. V. V. Zhikov, “Spectral Method in Homogenization Theory”, Tr. Mat. Inst. Steklova, 250 (2005),  95–104  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 250 (2005), 85–94
2004
31. V. V. Zhikov, “On gaps in the spectrum of some divergence elliptic operators with periodic coefficients”, Algebra i Analiz, 16:5 (2004),  34–58  mathnet  mathscinet  zmath; St. Petersburg Math. J., 16:5 (2005), 773–790
32. V. V. Zhikov, “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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 38:3 (2004), 173–183  isi  scopus
33. V. V. Zhikov, “On density of smooth functions in Sobolev–Orlich spaces”, Zap. Nauchn. Sem. POMI, 310 (2004),  67–81  mathnet  mathscinet  zmath  elib; J. Math. Sci. (N. Y.), 132:3 (2006), 285–294
2003
34. V. V. Zhikov, S. E. Pastukhova, “Homogenization for elasticity problems on periodic networks of critical thickness”, Mat. Sb., 194:5 (2003),  61–96  mathnet  mathscinet  zmath  elib; Sb. Math., 194:5 (2003), 697–732  isi  scopus
2002
35. V. V. Zhikov, “Homogenization of elasticity problems on singular structures”, Izv. RAN. Ser. Mat., 66:2 (2002),  81–148  mathnet  mathscinet  zmath  elib; Izv. Math., 66:2 (2002), 299–365  scopus
2001
36. V. V. Zhikov, “To the Problem of Passage to the Limit in Divergent Nonuniformly Elliptic Equations”, Funktsional. Anal. i Prilozhen., 35:1 (2001),  23–39  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 35:1 (2001), 19–33  isi  scopus
2000
37. V. V. Zhikov, “On an extension of the method of two-scale convergence and its applications”, Mat. Sb., 191:7 (2000),  31–72  mathnet  mathscinet  zmath  elib; Sb. Math., 191:7 (2000), 973–1014  isi  scopus
1999
38. V. V. Zhikov, “On the Homogenization Technique for Variational Problems”, Funktsional. Anal. i Prilozhen., 33:1 (1999),  14–29  mathnet  mathscinet  zmath; Funct. Anal. Appl., 33:1 (1999), 11–24  isi
1998
39. Yu. A. Alkhutov, V. V. Zhikov, “The leading term of the spectral asymptotics for the Kohn–Laplace operator in a bounded domain”, Mat. Zametki, 64:4 (1998),  493–505  mathnet  mathscinet  zmath; Math. Notes, 64:4 (1998), 429–439  isi
40. V. V. Zhikov, “Weighted Sobolev spaces”, Mat. Sb., 189:8 (1998),  27–58  mathnet  mathscinet  zmath; Sb. Math., 189:8 (1998), 1139–1170  isi  scopus
1997
41. V. V. Zhikov, “Meyer-type estimates for solving the nonlinear Stokes system”, Differ. Uravn., 33:1 (1997),  107–114  mathnet  mathscinet; Differ. Equ., 33:1 (1997), 108–115
42. V. V. Zhikov, “Diffusion in an Incompressible Random Flow”, Funktsional. Anal. i Prilozhen., 31:3 (1997),  10–22  mathnet  mathscinet  zmath; Funct. Anal. Appl., 31:3 (1997), 156–166  isi
43. V. V. Zhikov, M. E. Rychago, “Homogenization of non-linear second-order elliptic equations in perforated domains”, Izv. RAN. Ser. Mat., 61:1 (1997),  69–88  mathnet  mathscinet  zmath; Izv. Math., 61:1 (1997), 69–88  isi  scopus
1996
44. V. V. Zhikov, “Connectedness and homogenization. Examples of fractal conductivity”, Mat. Sb., 187:8 (1996),  3–40  mathnet  mathscinet  zmath; Sb. Math., 187:8 (1996), 1109–1147  isi  scopus
1993
45. V. V. Zhikov, “Asymptotic problems related to a second-order parabolic equation in nondivergence form with randomly homogeneous coefficients”, Differ. Uravn., 29:5 (1993),  859–869  mathnet  mathscinet; Differ. Equ., 29:5 (1993), 735–744
46. O. O. Barabanov, V. V. Zhikov, “The limit load and homogenization”, Izv. RAN. Ser. Mat., 57:5 (1993),  15–43  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 43:2 (1994), 205–231  isi
47. V. V. Zhikov, “Averaging in perforated random domains of general type”, Mat. Zametki, 53:1 (1993),  41–58  mathnet  mathscinet  zmath; Math. Notes, 53:1 (1993), 30–42  isi
1992
48. V. V. Zhikov, “Threshold of conductivity for a random cubic structure”, Mat. Zametki, 52:6 (1992),  15–24  mathnet  mathscinet  zmath; Math. Notes, 52:6 (1992), 1181–1187  isi
49. V. V. Zhikov, “On passage to the limit in nonlinear variational problems”, Mat. Sb., 183:8 (1992),  47–84  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 76:2 (1993), 427–459  isi
1991
50. V. V. Zhikov, “The Lavrent'ev effect and averaging of nonlinear variational problems”, Differ. Uravn., 27:1 (1991),  42–50  mathnet  mathscinet; Differ. Equ., 27:1 (1991), 32–39
51. V. V. Zhikov, “Estimates for the averaged matrix and the averaged tensor”, Uspekhi Mat. Nauk, 46:3(279) (1991),  49–109  mathnet  mathscinet  zmath; Russian Math. Surveys, 46:3 (1991), 65–136  isi
1990
52. V. V. Zhikov, “Problems of the continuation of functions in connection with averaging theory”, Differ. Uravn., 26:1 (1990),  39–50  mathnet  mathscinet; Differ. Equ., 26:1 (1990), 34–44
53. V. V. Zhikov, “Asymptotic problems connected with the heat equation in perforated domains”, Mat. Sb., 181:10 (1990),  1283–1305  mathnet  mathscinet  zmath; Math. USSR-Sb., 71:1 (1992), 125–147  isi
1989
54. V. V. Zhikov, “Spectral approach to asymptotic diffusion problems”, Differ. Uravn., 25:1 (1989),  44–50  mathnet  mathscinet; Differ. Equ., 25:1 (1989), 33–39
55. V. V. Zhikov, “Effective conductivity of random homogeneous sets”, Mat. Zametki, 45:4 (1989),  34–45  mathnet  mathscinet  zmath; Math. Notes, 45:4 (1989), 288–296  isi
56. V. V. Zhikov, “Remarks on the problem of residual diffusion”, Uspekhi Mat. Nauk, 44:6(270) (1989),  155–156  mathnet  mathscinet  zmath; Russian Math. Surveys, 44:6 (1989), 194–195  isi
1988
57. V. V. Zhikov, M. M. Sirazhudinov, “Averaging of a system of Beltrami equations”, Differ. Uravn., 24:1 (1988),  64–73  mathnet  mathscinet; Differ. Equ., 24:1 (1988), 50–56
1986
58. V. V. Zhikov, “Averaging of functionals of the calculus of variations and elasticity theory”, Izv. Akad. Nauk SSSR Ser. Mat., 50:4 (1986),  675–710  mathnet  mathscinet  zmath; Math. USSR-Izv., 29:1 (1987), 33–66
59. V. V. Zhikov, “Estimates for the trace of the averaged matrix”, Mat. Zametki, 40:2 (1986),  226–237  mathnet  mathscinet  zmath; Math. Notes, 40:2 (1986), 628–634  isi
1985
60. V. N. Denisov, V. V. Zhikov, “Stabilization of the solution of the Cauchy problem for parabolic equations”, Mat. Zametki, 37:6 (1985),  834–850  mathnet  mathscinet  zmath; Math. Notes, 37:6 (1985), 456–466  isi
1983
61. V. V. Zhikov, “Questions of convergence, duality, and averaging for functionals of the calculus of variations”, Izv. Akad. Nauk SSSR Ser. Mat., 47:5 (1983),  961–998  mathnet  mathscinet  zmath; Math. USSR-Izv., 23:2 (1984), 243–276
62. V. V. Zhikov, “Asymptotic behavior and stabilization of solutions of a second-order parabolic equation with lowest terms”, Tr. Mosk. Mat. Obs., 46 (1983),  69–98  mathnet  mathscinet  zmath
63. V. V. Zhikov, E. V. Krivenko, “Averaging of singularly perturbed elliptic operators”, Mat. Zametki, 33:4 (1983),  571–582  mathnet  mathscinet  zmath; Math. Notes, 33:4 (1983), 294–300  isi
64. V. V. Zhikov, “$G$-convergence of elliptic operators”, Mat. Zametki, 33:3 (1983),  345–356  mathnet  mathscinet  zmath; Math. Notes, 33:3 (1983), 174–181
1982
65. V. V. Zhikov, “Questions of convergence, duality, and averaging for a certain class of functionals in variational calculus”, Dokl. Akad. Nauk SSSR, 267:3 (1982),  524–528  mathnet  mathscinet  zmath
66. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, “Averaging of parabolic operators”, Tr. Mosk. Mat. Obs., 45 (1982),  182–236  mathnet  mathscinet  zmath
67. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, “Averaging of parabolic operators with almost periodic coefficients”, Mat. Sb. (N.S.), 117(159):1 (1982),  69–85  mathnet  mathscinet  zmath; Math. USSR-Sb., 45:1 (1983), 73–90
1981
68. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, “Theorems on the averaging of parabolic operators”, Dokl. Akad. Nauk SSSR, 260:3 (1981),  521–525  mathnet  mathscinet  zmath
69. V. V. Zhikov, M. M. Sirazhudinov, “On $G$-compactness of a class of nondivergence elliptic operators of second order”, Izv. Akad. Nauk SSSR Ser. Mat., 45:4 (1981),  718–733  mathnet  mathscinet  zmath; Math. USSR-Izv., 19:1 (1982), 27–40
70. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, “$G$-convergence of parabolic operators”, Uspekhi Mat. Nauk, 36:1(217) (1981),  11–58  mathnet  mathscinet  zmath; Russian Math. Surveys, 36:1 (1981), 9–60  isi
71. V. V. Zhikov, M. M. Sirazhudinov, “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  mathnet  mathscinet  zmath; Math. USSR-Sb., 44:2 (1983), 149–166
1979
72. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, Hà Tiên Ngoan, “Averaging and $G$-convergence of differential operators”, Uspekhi Mat. Nauk, 34:5(209) (1979),  65–133  mathnet  mathscinet  zmath; Russian Math. Surveys, 34:5 (1979), 69–147
73. V. V. Zhikov, “A point stabilization criterion for second order parabolic equations with almost periodic coefficients”, Mat. Sb. (N.S.), 110(152):2(10) (1979),  304–318  mathnet  mathscinet  zmath; Math. USSR-Sb., 38:2 (1981), 279–292  isi
1978
74. V. V. Zhikov, “Proof of the Favard theorem on the existence of almost-periodic solution for an arbitrary Banach space”, Mat. Zametki, 23:1 (1978),  121–126  mathnet  mathscinet  zmath; Math. Notes, 23:1 (1978), 66–69
1977
75. V. V. Zhikov, B. M. Levitan, “Favard theory”, Uspekhi Mat. Nauk, 32:2(194) (1977),  123–171  mathnet  mathscinet  zmath; Russian Math. Surveys, 32:1 (1977), 129–180
76. V. V. Zhikov, “On the stabilization of solutions of parabolic equations”, Mat. Sb. (N.S.), 104(146):4(12) (1977),  597–616  mathnet  mathscinet  zmath; Math. USSR-Sb., 33:4 (1977), 519–537  isi
1976
77. V. V. Zhikov, “Some admissibility and dichotomy questions. The averaging principle”, Izv. Akad. Nauk SSSR Ser. Mat., 40:6 (1976),  1380–1408  mathnet  mathscinet  zmath; Math. USSR-Izv., 10:6 (1976), 1307–1332
78. V. V. Zhikov, V. M. Tyurin, “The invertibility of the operator $d/dt+A(t)$ in the space of bounded functions”, Mat. Zametki, 19:1 (1976),  99–104  mathnet  mathscinet  zmath; Math. Notes, 19:1 (1976), 58–61
1975
79. V. V. Zhikov, “Solvability of linear equations in the Besicovitch and Bohr classes of almost periodic functions”, Mat. Zametki, 18:4 (1975),  553–560  mathnet  mathscinet; Math. Notes, 18:4 (1975), 918–922
80. V. V. Zhikov, “Some new results in abstract Favar theory”, Mat. Zametki, 17:1 (1975),  33–40  mathnet  mathscinet  zmath; Math. Notes, 17:1 (1975), 20–24
1973
81. V. V. Zhikov, “The averaging principle for parabolic equations with variable principal term”, Dokl. Akad. Nauk SSSR, 208:1 (1973),  32–35  mathnet  mathscinet  zmath
82. V. V. Zhikov, “Monotonicity in the theory of almost periodic solutions of nonlinear operator equations”, Mat. Sb. (N.S.), 90(132):2 (1973),  214–228  mathnet  mathscinet  zmath; Math. USSR-Sb., 19:2 (1973), 209–223
1972
83. V. V. Zhikov, “On the theory of admissibility of pairs of function spaces”, Dokl. Akad. Nauk SSSR, 205:6 (1972),  1281–1283  mathnet  mathscinet  zmath
84. V. V. Zhikov, “The stability and instability of Levinson's center”, Differ. Uravn., 8:12 (1972),  2167–2170  mathnet  mathscinet  zmath
1971
85. V. V. Zhikov, “Certain functional methods in the theory of almost periodic solutions. I”, Differ. Uravn., 7:2 (1971),  215–225  mathnet  mathscinet  zmath
86. V. V. Zhikov, “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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 5:1 (1971), 26–30
87. V. V. Zhikov, “The existence of Levitan almost-periodic solutions of linear systems (second complement to Favard's classical theory)”, Mat. Zametki, 9:4 (1971),  409–414  mathnet  mathscinet  zmath; Math. Notes, 9 (1971), 235–238
1970
88. V. V. Zhikov, “Almost periodic solutions of linear and nonlinear equations in a Banach space”, Dokl. Akad. Nauk SSSR, 195:2 (1970),  278–281  mathnet  mathscinet  zmath
89. V. V. Zhikov, “Addition to the classical theory of Favard”, Mat. Zametki, 7:2 (1970),  239–246  mathnet  mathscinet  zmath; Math. Notes, 7:2 (1970), 142–146
1968
90. V. V. Zhikov, “On a problem of Bochner and von Neumann”, Mat. Zametki, 3:5 (1968),  529–538  mathnet  mathscinet  zmath; Math. Notes, 3:5 (1968), 337–342
1967
91. V. V. Zhikov, “On inverse Sturm–Liouville problems on a finite segment”, Izv. Akad. Nauk SSSR Ser. Mat., 31:5 (1967),  965–976  mathnet  mathscinet  zmath; Math. USSR-Izv., 1:5 (1967), 923–934
92. M. G. Gasymov, V. V. Zhikov, B. M. Levitan, “Conditions for discreteness and finiteness of the negative spectrum of Schrödinger's operator equation”, Mat. Zametki, 2:5 (1967),  531–538  mathnet  mathscinet  zmath; Math. Notes, 2:5 (1967), 813–817
1966
93. V. V. Zhikov, “On the question of harmonic analysis of bounded solutions of operator equations”, Dokl. Akad. Nauk SSSR, 169:6 (1966),  1254–1257  mathnet  mathscinet  zmath
1965
94. V. V. Zhikov, “Almost periodic solutions of differential equations in Hilbert space”, Dokl. Akad. Nauk SSSR, 165:6 (1965),  1227–1230  mathnet  mathscinet  zmath
95. V. V. Zhikov, “Abstract equations with almost-periodic coefficients”, Dokl. Akad. Nauk SSSR, 163:3 (1965),  555–558  mathnet  mathscinet  zmath

2016
96. V. V. Zhikov, A. A. Shkalikov, “To the memory of Boris Moiseevich Levitan (on the 100th anniversary of his birth)”, Uspekhi Mat. Nauk, 71:3(429) (2016),  207–209  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 71:3 (2016), 601–603  isi
2014
97. V. V. Zhikov, A. A. Shkalikov, “In memory of Boris Moiseevich Levitan (1914–2004)”, Tr. Mosk. Mat. Obs., 75:2 (2014),  105–106  mathnet  elib; Trans. Moscow Math. Soc., 75 (2014), 87–88  scopus
2011
98. M. S. Agranovich, I. V. Astashova, L. A. Bagirov, V. V. Vlasov, V. V. Zhikov, Yu. S. Ilyashenko, V. V. Kozlov, A. A. Kon'kov, S. I. Pokhozhaev, E. V. Radkevich, N. Kh. Rozov, I. N. Sergeev, A. L. Skubachevskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Vladimir Alexandrovich Kondratiev. July 2, 1935 – March 11, 2010”, CMFD, 39 (2011),  5–10  mathnet  mathscinet; Journal of Mathematical Sciences, 190:1 (2013), 1–7
99. I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. Yu. Goritskii, N. V. Denisova, V. V. Zhikov, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, E. V. Radkevich, O. S. Rozanova, È. R. Rozendorn, N. Kh. Rozov, M. S. Romanov, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Olga Arsenjevna Oleinik”, Tr. Semim. im. I. G. Petrovskogo, 28 (2011),  5–7  mathnet  elib; J. Math. Sci. (N. Y.), 179:3 (2011), 345–346
2003
100. T. D. Venttsel', V. S. Vladimirov, V. V. Zhikov, A. M. Il'in, V. A. Il'in, V. A. Kondrat'ev, L. D. Kudryavtsev, E. F. Mishchenko, S. M. Nikol'skii, Yu. S. Osipov, E. V. Radkevich, N. Kh. Rozov, V. A. Sadovnichii, L. D. Faddeev, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, A. A. Shkalikov, “Ol'ga Arsen'evna Oleinik (obituary)”, Uspekhi Mat. Nauk, 58:1(349) (2003),  165–174  mathnet  mathscinet  zmath; Russian Math. Surveys, 58:1 (2003), 161–172  isi
1996
101. N. S. Bakhvalov, A. Yu. Belyaev, M. I. Vishik, V. V. Zhikov, V. P. Maslov, O. A. Oleinik, G. P. Panasenko, A. L. Piatnitski, “Sergei Mikhailovich Kozlov (obituary)”, Uspekhi Mat. Nauk, 51:4(310) (1996),  145–146  mathnet  mathscinet; Russian Math. Surveys, 51:4 (1996), 723–725  isi

Presentations in Math-Net.Ru
1. Spectral problems in some models of photonic crystals
V. V. Zhikov
International Conference on Differential Equations and Dynamical Systems
July 9, 2014 10:30
2. Соболевские пространства с переменным показателем, эффект Лаврентьева, неклассические эллиптические задачи
V. V. Zhikov
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
November 2, 2011 16:00
3. On an approach to solvability of generalized Navier–Stokes equations
V. V. Zhikov
Meetings of the Moscow Mathematical Society
December 9, 2008
4. Вариационные задачи и эллиптические уравнения с нестандартными условиями роста
V. V. Zhikov
Meetings of the Moscow Mathematical Society
April 18, 2006

Organisations
 
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