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## Zhikov, Vasiliĭ Vasil’evich

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 Author ID: zhikov.vasilii-vasilevich Published as: Jikov, V.; Jikov, V. V.; Jikov, Vasili V.; Jikov, Vasilii V.; Zhikov, V. V.; Zhikov, Vasilii; Zhikov, Vasilii V.; Zhikov, Vasilii Vasil’evich; Zhikov, Vasilij V.; Zhikov, Vasiliĭ V.; Zhikov, Vasily; Zhikov, Vasily V.; Zhikov, Vassily; Zikov, V. V. External Links: MGP · Math-Net.Ru · Wikidata · GND
 Documents Indexed: 207 Publications since 1965, including 5 Books Biographic References: 6 Publications
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#### Co-Authors

 98 single-authored 38 Pastukhova, Svetlana Evgenievna 15 Oleĭnik, Ol’ga Arsen’evna 10 Alkhutov, Yuriy Alexandrovich 10 Kozlov, Sergei M. 5 Levitan, Boris Moiseevich 5 Sirazhudinov, Magomed M. 4 Surnachëv, Mikhaĭl Dmitrievich 3 Kozlov, Serguei M. 3 Piatnitski, Andrey L. 3 Rychago, M. E. 3 Shkalikov, Andreĭ Andreevich 2 Boles Basit, R. 2 Cardone, Gennaro 2 Chechkin, Gregory A. 2 Corbo Esposito, Antonio 2 Ha Tien Ngoan 2 Lukkassen, Dag 2 Tikhomirova, S. V. 2 Yosifian, G. A. 1 Agranovich, Mikhail Semënovich 1 Altukhov, Yu. A. 1 Antontsev, S. V. 1 Antontsev, Stanislav Nikolaevich 1 Astashova, Irina V. 1 Bagirov, Lev A. 1 Barabanov, O. O. 1 Beliaev, Alexei 1 Berdichevskiĭ, Viktor L’vovich 1 Biroli, Marco 1 Cardone, Giuseppe 1 Cherednichenko, Kirill D. 1 Denisov, Vasiliĭ Nikolaevich 1 Esposito, A. Corbo 1 Gasymov, M. G. 1 Ilyashenko, Yulij Sergeevich 1 Kon’kov, Andrej A. 1 Kostyuchenko, Anatolii Gordeevich 1 Kozlov, Valeriĭ Vasil’evich 1 Krivenko, E. V. 1 Marchenko, Vladimir Aleksandrovich 1 Maslov, Klavdii V. 1 Maslov, Viktor Pavlovich 1 Papanicolaou, George C. 1 Pokhozhaev, Stanislav I. 1 Radkevich, Evgeniĭ Vladimirovich 1 Rozov, Nikolaĭ Khristovich 1 Sadovnichiĭ, Viktor Antonovich 1 Sargsyan, I. S. 1 Sergeev, Igor N. 1 Shamaev, Alexei S. 1 Shaposhnikova, Tatiana A. 1 Shepelsky, Dmitry 1 Shul’ga, S. B. 1 Skubachevskii, Aleksandr L. 1 Smyshlyaev, Valery P. 1 Tchou, Nicoletta Anna 1 Tyurin, V. M. 1 Venttsel’, T. D. 1 Vladimirov, Vasiliĭ Sergeevich 1 Vlasov, Viktor Valentinovich 1 Yakubovich, D. A.
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all top 5

#### Fields

 140 Partial differential equations (35-XX) 33 Calculus of variations and optimal control; optimization (49-XX) 32 Mechanics of deformable solids (74-XX) 29 Ordinary differential equations (34-XX) 26 Operator theory (47-XX) 14 Fluid mechanics (76-XX) 13 Functional analysis (46-XX) 7 History and biography (01-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Probability theory and stochastic processes (60-XX) 5 Measure and integration (28-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 General and overarching topics; collections (00-XX) 3 Abstract harmonic analysis (43-XX) 2 Integral equations (45-XX) 2 General topology (54-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX)

#### Citations contained in zbMATH

149 Publications have been cited 2,968 times in 1,937 Documents Cited by Year
Averaging of functionals of the calculus of variations and elasticity theory. Zbl 0599.49031
Zhikov, V. V.
1987
Almost periodic functions and differential equations. Zbl 0499.43005
Levitan, B. M.; Zhikov, V. V.
1982
Homogenization of differential operators. Zbl 0801.35001
Jikov, V. V.; Kozlov, S. M.; Oleĭnik, O. A.
1993
On Lavrentiev’s phenomenon. Zbl 0910.49020
Zhikov, Vasiliĭ V.
1995
On some variational problems. Zbl 0917.49006
Zhikov, Vasilij V.
1997
Homogenization of differential operators and integral functionals. Transl. from the Russian by G. A. Yosifian. Zbl 0838.35001
Zhikov, V. V.; Kozlov, S. M.; Olejnik, O. A.
1994
Almost periodic functions and differential equations. (Pochti- periodicheskie funktsii i differentsial’nye uravneniya). Zbl 0414.43008
Levitan, B. M.; Zhikov, V. V.
1978
On an extension of the method of two-scale convergence and its applications. Zbl 0969.35048
Zhikov, V. V.
2000
On the density of smooth functions in Sobolev-Orlicz spaces. Zbl 1086.46026
Zhikov, V. V.
2004
Weighted Sobolev spaces. Zbl 0919.46026
Zhikov, V. V.
1998
Averaging and G-convergence of differential operators. Zbl 0445.35096
Zhikov, V. V.; Kozlov, S. M.; Oleĭnik, O. A.; Hà Tiên Ngoan
1979
On operator estimates for some problems in homogenization theory. Zbl 1387.35037
Zhikov, V. V.; Pastukhova, S. E.
2005
Higher integrability for parabolic equations of $$p(x,t)$$-Laplacian type. Zbl 1122.35043
Antontsev, Stanislav; Zhikov, Vasilii
2005
Homogenization of elasticity problems on singular structures. Zbl 1043.35031
Zhikov, V. V.
2002
Meyers type estimates for the solution of a nonlinear Stokes system. Zbl 0911.35089
Zhikov, V. V.
1997
On the passage to the limit in nonlinear variational problems. Zbl 0767.35021
Zhikov, V. V.
1992
Estimates of homogenization for a parabolic equation with periodic coefficients. Zbl 1129.35012
Zhikov, V. V.; Pastukhova, S. E.
2006
On variational problems and nonlinear elliptic equations with nonstandard growth conditions. Zbl 1279.49005
Zhikov, V. V.
2011
On operator estimates in homogenization theory. Zbl 1130.35312
Zhikov, V. V.
2005
Some estimates from homogenization theory. Zbl 1155.35311
Zhikov, V. V.
2006
On two-scale convergence. Zbl 1284.35054
Zhikov, V. V.
2003
Solvability of the three-dimensional thermistor problem. Zbl 1237.35058
Zhikov, V. V.
2008
Non-local homogenized limits for composite media with highly anisotropic periodic fibres. Zbl 1101.74024
Cherednichenko, K. D.; Smyshlyaev, V. P.; Zhikov, V. V.
2006
Connectedness and homogenization. Examples of fractal conductivity. Zbl 0874.35011
Zhikov, V. V.
1996
G-convergence of parabolic operators. Zbl 0479.35047
Zhikov, V. V.; Kozlov, S. M.; Oleĭnik, O. A.
1981
Operator estimates in homogenization theory. Zbl 1354.35028
Zhikov, V. V.; Pastukhova, S. E.
2016
Averaging of problems in the theory of elasticity on periodic grids of critical thickness. Zbl 1077.35023
Zhikov, V. V.; Pastukhova, S. E.
2003
Lavrentiev phenomenon and homogenization for some variational problems. Zbl 0783.35005
Zhikov, Vasily
1993
On the property of higher integrability for parabolic systems of variable order of nonlinearity. Zbl 1204.35060
Zhikov, V. V.; Pastukhova, S. E.
2010
On the technique for passing to the limit in nonlinear elliptic equations. Zbl 1271.35033
Zhikov, V. V.
2009
Homogenization of degenerate elliptic equations. Zbl 1164.35009
Zhikov, V. V.; Pastukhova, S. E.
2008
On gaps in the spectrum of some elliptic operators in divergent form with periodic coefficients. Zbl 1174.35458
Zhikov, V. V.
2005
Spectral approach to asymptotic problems in diffusion. Zbl 0695.35014
Zhikov, V. V.
1989
Averaging of singularly perturbed elliptic operators. Zbl 0556.35003
Zhikov, V. V.; Krivenko, E. V.
1983
Questions of convergence, duality, and averaging for functionals of the calculus of variations. Zbl 0551.49012
Zhikov, V. V.
1984
Averaging and $$G$$-convergence of differential operators. Zbl 0421.35076
Zhikov, V. V.; Kozlov, S. M.; Oleĭnik, O. A.; Hà Tiên Ngoan
1979
Favard theory. Zbl 0378.34049
Zikov, V. V.; Levitan, B. M.
1977
Parabolic equations with variable order of nonlinearity. Zbl 1199.35020
Altukhov, Yu. A.; Antontsev, S. V.; Zhikov, V. V.
2009
Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent. Zbl 1172.35024
Zhikov, V. V.; Pastukhova, S. E.
2008
On passage to the limit in nonlinear variational problems. Zbl 0791.35036
Zhikov, V. V.
1992
Remarks on the uniqueness of a solution of the Dirichlet problem for second-order elliptic equations with lower-order terms. Zbl 1147.35302
Zhikov, V. V.
2004
To the problem of passage to the limit in divergent nonuniformly elliptic equations. Zbl 1085.35054
Zhikov, V. V.
2001
Existence theorems for solutions of parabolic equations with variable order of nonlinearity. Zbl 1213.35262
Alkhutov, Yu. A.; Zhikov, V. V.
2010
On passage to the limit in nonlinear elliptic equations. Zbl 1184.35131
Zhikov, V. V.
2008
Questions of convergence, duality, and averaging for functionals of calculus of variations. Zbl 0534.49014
Zhikov, V. V.
1983
New approach to the solvability of generalized Navier-Stokes equations. Zbl 1271.35061
Zhikov, V. V.
2009
Homogenization of random singular structures and random measures. Zbl 1113.35021
Zhikov, V. V.; Pyatniskii, A. L.
2006
Spectral method in homogenization theory. Zbl 1127.35311
Zhikov, V. V.
2005
Lavrent’ev effect and the averaging of nonlinear variational problems. Zbl 0749.49022
Zhikov, V. V.
1991
Estimates for the averaged matrix and the averaged tensor. Zbl 0751.15014
Zhikov, V. V.
1991
On the homogenization of degenerate elliptic equations. Zbl 1152.35044
Zhikov, V. V.; Pastukhova, S. E.; Tikhomirova, S. V.
2006
On homogenization of networks and junctions. Zbl 1031.35018
Chechkin, Gregory A.; Jikov, Vasili V.; Lukkassen, Dag; Piatnitski, Andrey L.
2002
On the G-convergence of parabolic operators. Zbl 0467.35056
Zhikov, V. V.; Kozlov, S. M.; Oleĭnik, O. A.
1981
Existence theorem for some pairs of coupled elliptic equations. Zbl 1180.35224
Zhikov, V. V.
2008
On the compensated compactness principle. Zbl 1211.35075
Zhikov, V. V.; Pastukhova, S. E.
2010
On a homogenization technique for variational problems. Zbl 0959.49016
Zhikov, V. V.
1999
On the homogenization of nonlinear variational problems in perforated domains. Zbl 0914.35014
Zhikov, Vasilii V.
1994
Asymptotic behavior and stabilization of the solutions of a second order parabolic equation with lower terms. Zbl 0557.35060
Zhikov, V. V.
1983
Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent. Zbl 1295.35289
Alkhutov, Yu A.; Zhikov, V. V.
2014
On the solvability of the Navier-Stokes equations for a compressible non-Newtonian fluid. Zbl 1387.35509
Zhikov, V. V.; Pastukhova, S. E.
2009
Density of smooth functions in weighted Sobolev spaces. Zbl 1303.46027
Zhikov, V. V.
2013
On gaps in the spectrum of the operator of elasticity theory on a high contrast periodic structure. Zbl 1302.35362
Zhikov, V. V.; Pastukhova, S. E.
2013
Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent. Zbl 1291.35110
Alkhutov, Yu. A.; Zhikov, V. V.
2011
Homogenization of monotone operators under conditions of coercitivity and growth of variable order. Zbl 1237.35012
Zhikov, V. V.; Pastukhova, S. E.
2011
Averaging of parabolic operators. Zbl 0576.35052
Zhikov, V. V.; Kozlov, S. M.; Olejnik, O. A.
1984
On the Trotter–Kato theorem in a variable space. Zbl 1158.47027
Zhikov, V. V.; Pastukhova, S. E.
2007
On the Hölder property of solutions of degenerate elliptic equations. Zbl 1090.35510
Alkhutov, Yu. A.; Zhikov, V. V.
2001
Diffusion in an incompressible random flow. Zbl 0902.35127
Zhikov, V. V.
1997
On Lavrent’ev’s effect. Zbl 0919.49010
Zhikov, V. V.
1995
Averaging in perforated random domains of general type. Zbl 0801.60058
Zhikov, V. V.
1993
Averaging of parabolic operators. Zbl 0531.35041
Zhikov, V. V.; Kozlov, S. M.; Olejnik, O. A.
1982
Averaging of parabolic operators with almost periodic coefficients. Zbl 0487.35050
Zhikov, V. V.; Kozlov, S. M.; Oleĭnik, O. A.
1982
Beweis eines Satzes von Favard über die Existenz einer fastperiodischen Lösung im Fall eines beliebigen Banachraumes. Zbl 0375.34037
Zikov, V. V.
1978
Bloch principle for elliptic differential operators with periodic coefficients. Zbl 1351.35026
Zhikov, V. V.; Pastukhova, S. E.
2016
The $$\Gamma$$-convergence of oscillating integrands with nonstandard coercivity and growth conditions. Zbl 1293.49031
Zhikov, V. V.; Pastukhova, S. E.
2014
On existence and uniqueness classes for the Cauchy problem for parabolic equations of the $$p$$-Laplace type. Zbl 1267.35102
Surnachev, Mikhail D.; Zhikov, Vasily V.
2013
Lemmas on compensated compactness in elliptic and parabolic equations. Zbl 1216.35045
Zhikov, V. V.; Pastukhova, S. E.
2010
On the weak convergence of fluxes to a flux. Zbl 1202.35094
Zhikov, V. V.
2010
A note on Sobolev spaces. Zbl 1098.46028
Zhikov, V. V.
2003
Homogenization of elasticity problems on periodic lattices of critical thickness. Zbl 1146.35310
Zhikov, V. V.; Pastukhova, S. E.
2002
Averaging of problems in the theory of elasticity on singular structures. Zbl 1090.35505
Zhikov, V. V.
2001
On the homogenization of elliptic operators with almost-periodic coefficients. Zbl 0568.35029
Olejnik, O. A.; Zhikov, V. V.
1982
On the stabilization of solutions of parabolic equations. Zbl 0398.35048
Zikov, V. V.
1977
Homogenization estimates of operator type for an elliptic equation with quasiperiodic coefficients. Zbl 1327.35082
Pastukhova, S. E.; Zhikov, V. V.
2015
Gamma-convergence of integrands with nonstandard coercivity and growth conditions. Zbl 1301.49034
Zhikov, V. V.; Pastukhova, S. E.
2014
Estimates of the Nash-Aronson type for degenerating parabolic equations. Zbl 1277.35224
Zhikov, V. V.
2013
Homogenization of a Navier-Stokes-type system for electrorheological fluid. Zbl 1228.35032
Zhikov, V. V.
2011
Existence theorems and qualitative properties of solutions to parabolic equations with a variable order of nonlinearity. Zbl 1203.35146
Alkhutov, Yu. A.; Zhikov, V. V.
2010
A class of degenerate elliptic equations. Zbl 1205.35119
Alkhutov, Yu. A.; Zhikov, V. V.
2003
Effective conductivity of homogeneous random sets. Zbl 0688.60075
Zhikov, V. V.
1989
Averaging of non-divergent second order elliptic and parabolic operators and stabilization of the solution of the Cauchy problem. Zbl 0472.35021
Zhikov, V. V.; Sirazhudinov, M. M.
1981
Conditions for the negative spectrum of the Schrödinger equation operator to be discrete and finite. Zbl 0159.19801
Gasymov, M. G.; Zhikov, V. V.; Levitan, B. M.
1967
Galerkin approximations in problems with $$p$$-Laplacian. Zbl 1360.35061
Zhikov, V. V.; Yakubovich, D. A.
2016
On density of smooth functions in weighted Sobolev spaces with variable exponents. Zbl 1354.46039
Zhikov, V. V.; Surnachev, M. D.
2016
Introduction to the theory of two-scale convergence. Zbl 1328.46029
Zhikov, V. V.; Yosifian, G. A.
2014
Stabilization of solutions to nonlinear parabolic equations of the $$p$$-Laplace type. Zbl 1330.35205
Surnachev, M. D.; Zhikov, V. V.
2013
Parabolic lemmas on compensated compactness and their applications. Zbl 1203.35148
Zhikov, V. V.; Pastukhova, S. E.
2010
On operator estimates in nonsymmetric averaging problems. Zbl 1181.35020
Zhikov, V. V.; Tikhomirova, S. V.
2007
Homogenization of monotone operators by the method of two-scale convergence. Zbl 1120.35010
Zhikov, V. V.; Rychago, M. E.; Shul’ga, S. B.
2005
On the Korn inequalities on thin periodic frames. Zbl 1072.74056
Zhikov, V. V.; Pastukhova, S. E.
2004
Homogenization and two-scale convergence in the Sobolev space with an oscillating exponent. Zbl 1415.35030
Zhikov, V. V.; Pastukhova, S. E.
2019
Operator estimates in homogenization theory. Zbl 1354.35028
Zhikov, V. V.; Pastukhova, S. E.
2016
Bloch principle for elliptic differential operators with periodic coefficients. Zbl 1351.35026
Zhikov, V. V.; Pastukhova, S. E.
2016
Galerkin approximations in problems with $$p$$-Laplacian. Zbl 1360.35061
Zhikov, V. V.; Yakubovich, D. A.
2016
On density of smooth functions in weighted Sobolev spaces with variable exponents. Zbl 1354.46039
Zhikov, V. V.; Surnachev, M. D.
2016
Homogenization estimates of operator type for an elliptic equation with quasiperiodic coefficients. Zbl 1327.35082
Pastukhova, S. E.; Zhikov, V. V.
2015
Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent. Zbl 1295.35289
Alkhutov, Yu A.; Zhikov, V. V.
2014
The $$\Gamma$$-convergence of oscillating integrands with nonstandard coercivity and growth conditions. Zbl 1293.49031
Zhikov, V. V.; Pastukhova, S. E.
2014
Gamma-convergence of integrands with nonstandard coercivity and growth conditions. Zbl 1301.49034
Zhikov, V. V.; Pastukhova, S. E.
2014
Introduction to the theory of two-scale convergence. Zbl 1328.46029
Zhikov, V. V.; Yosifian, G. A.
2014
Uniform convexity and variational convergence. Zbl 1321.49026
Zhikov, Vasilii Vasil’evich; Pastukhova, Svetlana Evgenievna
2014
Density of smooth functions in weighted Sobolev spaces. Zbl 1303.46027
Zhikov, V. V.
2013
On gaps in the spectrum of the operator of elasticity theory on a high contrast periodic structure. Zbl 1302.35362
Zhikov, V. V.; Pastukhova, S. E.
2013
On existence and uniqueness classes for the Cauchy problem for parabolic equations of the $$p$$-Laplace type. Zbl 1267.35102
Surnachev, Mikhail D.; Zhikov, Vasily V.
2013
Estimates of the Nash-Aronson type for degenerating parabolic equations. Zbl 1277.35224
Zhikov, V. V.
2013
Stabilization of solutions to nonlinear parabolic equations of the $$p$$-Laplace type. Zbl 1330.35205
Surnachev, M. D.; Zhikov, V. V.
2013
Vladimir Alexandrovich Kondratiev. July 2, 1935–March 11, 2010. Zbl 1277.01013
Agranovich, M. S.; Astashova, I. V.; Bagirov, L. A.; Vlasov, V. V.; Zhikov, V. V.; Ilyashenko, Yu. S.; Kozlov, V. V.; Kon’kov, A. A; Pokhozhaev, S. I.; Radkevich, E. V.; Rozov, N. Kh.; Sergeev, I. N.; Skubachevskii, A. L.; Chechkin, G. A.; Shamaev, A. S.; Shaposhnikova, T. A.
2013
On the Navier-Stokes equations: existence theorems and energy equalities. Zbl 1303.35062
Zhikov, V. V.; Pastukhova, S. E.
2012
On existence and uniqueness classes for the Cauchy problem for the parabolic $$p$$-Laplace equation. Zbl 1269.35016
Zhikov, V. V.; Surnachev, M. D.
2012
On variational problems and nonlinear elliptic equations with nonstandard growth conditions. Zbl 1279.49005
Zhikov, V. V.
2011
Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent. Zbl 1291.35110
Alkhutov, Yu. A.; Zhikov, V. V.
2011
Homogenization of monotone operators under conditions of coercitivity and growth of variable order. Zbl 1237.35012
Zhikov, V. V.; Pastukhova, S. E.
2011
Homogenization of a Navier-Stokes-type system for electrorheological fluid. Zbl 1228.35032
Zhikov, V. V.
2011
On the property of higher integrability for parabolic systems of variable order of nonlinearity. Zbl 1204.35060
Zhikov, V. V.; Pastukhova, S. E.
2010
Existence theorems for solutions of parabolic equations with variable order of nonlinearity. Zbl 1213.35262
Alkhutov, Yu. A.; Zhikov, V. V.
2010
On the compensated compactness principle. Zbl 1211.35075
Zhikov, V. V.; Pastukhova, S. E.
2010
Lemmas on compensated compactness in elliptic and parabolic equations. Zbl 1216.35045
Zhikov, V. V.; Pastukhova, S. E.
2010
On the weak convergence of fluxes to a flux. Zbl 1202.35094
Zhikov, V. V.
2010
Existence theorems and qualitative properties of solutions to parabolic equations with a variable order of nonlinearity. Zbl 1203.35146
Alkhutov, Yu. A.; Zhikov, V. V.
2010
Parabolic lemmas on compensated compactness and their applications. Zbl 1203.35148
Zhikov, V. V.; Pastukhova, S. E.
2010
On the technique for passing to the limit in nonlinear elliptic equations. Zbl 1271.35033
Zhikov, V. V.
2009
Parabolic equations with variable order of nonlinearity. Zbl 1199.35020
Altukhov, Yu. A.; Antontsev, S. V.; Zhikov, V. V.
2009
New approach to the solvability of generalized Navier-Stokes equations. Zbl 1271.35061
Zhikov, V. V.
2009
On the solvability of the Navier-Stokes equations for a compressible non-Newtonian fluid. Zbl 1387.35509
Zhikov, V. V.; Pastukhova, S. E.
2009
Solvability of the three-dimensional thermistor problem. Zbl 1237.35058
Zhikov, V. V.
2008
Homogenization of degenerate elliptic equations. Zbl 1164.35009
Zhikov, V. V.; Pastukhova, S. E.
2008
Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent. Zbl 1172.35024
Zhikov, V. V.; Pastukhova, S. E.
2008
On passage to the limit in nonlinear elliptic equations. Zbl 1184.35131
Zhikov, V. V.
2008
Existence theorem for some pairs of coupled elliptic equations. Zbl 1180.35224
Zhikov, V. V.
2008
Solvability of generalized Navier-Stokes equations. Zbl 1217.35139
Zhikov, V. V.
2008
On Gehring’s Lemma. Zbl 1172.35023
Zhikov, V. V.; Pastukhova, S. E.
2008
On the Trotter–Kato theorem in a variable space. Zbl 1158.47027
Zhikov, V. V.; Pastukhova, S. E.
2007
On operator estimates in nonsymmetric averaging problems. Zbl 1181.35020
Zhikov, V. V.; Tikhomirova, S. V.
2007
Estimates of homogenization for a parabolic equation with periodic coefficients. Zbl 1129.35012
Zhikov, V. V.; Pastukhova, S. E.
2006
Some estimates from homogenization theory. Zbl 1155.35311
Zhikov, V. V.
2006
Non-local homogenized limits for composite media with highly anisotropic periodic fibres. Zbl 1101.74024
Cherednichenko, K. D.; Smyshlyaev, V. P.; Zhikov, V. V.
2006
Homogenization of random singular structures and random measures. Zbl 1113.35021
Zhikov, V. V.; Pyatniskii, A. L.
2006
On the homogenization of degenerate elliptic equations. Zbl 1152.35044
Zhikov, V. V.; Pastukhova, S. E.; Tikhomirova, S. V.
2006
Estimates of Nash-Aronson type for a diffusion equation with asymmetric matrix and their applications to homogenization. Zbl 1160.35360
Zhikov, V. V.
2006
Derivation of the limit equations of elasticity theory on thin nets. Zbl 1109.74033
Zhikov, V. V.; Pastukhova, S. E.
2006
In memory of Boris Levitan. Zbl 1118.01308
Kostyuchenko, A. G.; Maslov, V. P.; Sadovnichii, V. A.; Sargsyan, I. S.; Shkalikov, A. A.; Zhikov, V. V.
2006
On operator estimates for some problems in homogenization theory. Zbl 1387.35037
Zhikov, V. V.; Pastukhova, S. E.
2005
Higher integrability for parabolic equations of $$p(x,t)$$-Laplacian type. Zbl 1122.35043
Antontsev, Stanislav; Zhikov, Vasilii
2005
On operator estimates in homogenization theory. Zbl 1130.35312
Zhikov, V. V.
2005
On gaps in the spectrum of some elliptic operators in divergent form with periodic coefficients. Zbl 1174.35458
Zhikov, V. V.
2005
Spectral method in homogenization theory. Zbl 1127.35311
Zhikov, V. V.
2005
Homogenization of monotone operators by the method of two-scale convergence. Zbl 1120.35010
Zhikov, V. V.; Rychago, M. E.; Shul’ga, S. B.
2005
Homogenized tensor on networks. Zbl 1138.74380
Zhikov, V. V.; Pastukhova, S. E.
2005
On the density of smooth functions in Sobolev-Orlicz spaces. Zbl 1086.46026
Zhikov, V. V.
2004
Remarks on the uniqueness of a solution of the Dirichlet problem for second-order elliptic equations with lower-order terms. Zbl 1147.35302
Zhikov, V. V.
2004
On the Korn inequalities on thin periodic frames. Zbl 1072.74056
Zhikov, V. V.; Pastukhova, S. E.
2004
Homogenization of some problems with gradient constraints. Zbl 1077.35014
Cardone, G.; Corbo Esposito, A.; Yosifian, G. A.; Zhikov, V. V.
2004
On two-scale convergence. Zbl 1284.35054
Zhikov, V. V.
2003
Averaging of problems in the theory of elasticity on periodic grids of critical thickness. Zbl 1077.35023
Zhikov, V. V.; Pastukhova, S. E.
2003
A note on Sobolev spaces. Zbl 1098.46028
Zhikov, V. V.
2003
A class of degenerate elliptic equations. Zbl 1205.35119
Alkhutov, Yu. A.; Zhikov, V. V.
2003
Korn inequalities for thin periodic structures. Zbl 1246.35031
Zhikov, Vasilii V.; Pastukhova, Svetlana E.
2003
On the Hölder property of one elliptic equation. Zbl 1137.35383
Alkhutov, Yu. A.; Zhikov, V. V.
2003
Homogenization on periodic lattices. Zbl 1124.35306
Zhikov, V. V.; Pastukhova, S. E.
2003
Homogenization of elasticity problems on singular structures. Zbl 1043.35031
Zhikov, V. V.
2002
On homogenization of networks and junctions. Zbl 1031.35018
Chechkin, Gregory A.; Jikov, Vasili V.; Lukkassen, Dag; Piatnitski, Andrey L.
2002
Homogenization of elasticity problems on periodic lattices of critical thickness. Zbl 1146.35310
Zhikov, V. V.; Pastukhova, S. E.
2002
To the problem of passage to the limit in divergent nonuniformly elliptic equations. Zbl 1085.35054
Zhikov, V. V.
2001
On the Hölder property of solutions of degenerate elliptic equations. Zbl 1090.35510
Alkhutov, Yu. A.; Zhikov, V. V.
2001
Averaging of problems in the theory of elasticity on singular structures. Zbl 1090.35505
Zhikov, V. V.
2001
On an extension of the method of two-scale convergence and its applications. Zbl 0969.35048
Zhikov, V. V.
2000
The fundamental theorem of arithmetic. Zbl 0951.00005
Zhikov, V. V.
2000
On a homogenization technique for variational problems. Zbl 0959.49016
Zhikov, V. V.
1999
Homogenization for Heisenberg operator with Neumann boundary conditions. Zbl 0933.35021
Biroli, M.; Tchou, N. A.; Zhikov, V. V.
1999
Homogenization. In memory of Serguei Kozlov. Zbl 0924.00012
Berdichevsky, V. (ed.); Jikov, V. (ed.); Papanicolaou, G. (ed.)
1999
Multiscaled homogenization. Zbl 1041.35010
Jikov, V. V.; Kozlov, S. M.
1999
Weighted Sobolev spaces. Zbl 0919.46026
Zhikov, V. V.
1998
On some variational problems. Zbl 0917.49006
Zhikov, Vasilij V.
1997
Meyers type estimates for the solution of a nonlinear Stokes system. Zbl 0911.35089
Zhikov, V. V.
1997
Diffusion in an incompressible random flow. Zbl 0902.35127
Zhikov, V. V.
1997
Homogenization of nonlinear second-order elliptic equations in perforated domains. Zbl 0884.35008
Zhikov, V. V.; Rychago, M. E.
1997
Connectedness and homogenization. Examples of fractal conductivity. Zbl 0874.35011
Zhikov, V. V.
1996
On Lavrentiev’s phenomenon. Zbl 0910.49020
Zhikov, Vasiliĭ V.
1995
On Lavrent’ev’s effect. Zbl 0919.49010
Zhikov, V. V.
1995
Connectedness and homogenization. Examples of the fractal conductivity. Zbl 0900.35038
Zhikov, V. V.
1995
Homogenization of differential operators and integral functionals. Transl. from the Russian by G. A. Yosifian. Zbl 0838.35001
Zhikov, V. V.; Kozlov, S. M.; Olejnik, O. A.
1994
On the homogenization of nonlinear variational problems in perforated domains. Zbl 0914.35014
Zhikov, Vasilii V.
1994
On the homogenization of the system of Stokes equations in a porous medium. Zbl 0835.35112
Zhikov, V. V.
1994
Homogenization of differential operators. Zbl 0801.35001
Jikov, V. V.; Kozlov, S. M.; Oleĭnik, O. A.
1993
Lavrentiev phenomenon and homogenization for some variational problems. Zbl 0783.35005
Zhikov, Vasily
1993
Averaging in perforated random domains of general type. Zbl 0801.60058
Zhikov, V. V.
1993
On the passage to the limit in nonlinear variational problems. Zbl 0767.35021
Zhikov, V. V.
1992
On passage to the limit in nonlinear variational problems. Zbl 0791.35036
Zhikov, V. V.
1992
Asymptotic problems connected with the heat equation in perforated domains. Zbl 0774.35028
Zhikov, V. V.
1992
Errata to: “Estimates for the averaged matrix and the averaged tensor”. Zbl 0793.15012
Zhikov, V. V.
1992
...and 49 more Documents
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#### Cited by 1,801 Authors

 63 Zhikov, Vasiliĭ Vasil’evich 57 Pastukhova, Svetlana Evgenievna 44 Zhang, Qihu 39 Rădulescu, Vicenţiu D. 31 Papageorgiou, Nikolaos S. 31 Suslina, Tat’yana Aleksandrovna 25 Fan, Xianling 25 Piatnitski, Andrey L. 23 Alkhutov, Yuriy Alexandrovich 20 Antontsev, Stanislav Nikolaevich 20 Nguyen Van Minh 19 Cherednichenko, Kirill D. 17 Cheban, David Nikolai 17 Dai, Guowei 17 Mihăilescu, Mihai 17 Mingione, Giuseppe 16 Ge, Bin 16 Repovš, Dušan D. 16 Surnachëv, Mikhaĭl Dmitrievich 15 Baskakov, Anatoliĭ Grigor’evich 15 Nazarov, Sergeĭ Aleksandrovich 15 Ok, Jihoon 14 Galewski, Marek 13 Afrouzi, Ghasem Alizadeh 13 Byun, Sun-Sig 13 Harjulehto, Petteri 13 Kogut, Peter I. 13 Zhan, Huashui 12 Borisov, Denis Ivanovich 12 Yuan, Rong 11 Cao, Liqun 11 Cardone, Giuseppe 11 Hästö, Peter A. 11 Liu, Xiaopin 11 Qiu, Zhimei 11 Shmarev, Sergey I. 11 Woukeng, Jean Louis 10 Allaoui, Mostafa 10 Barreira, Luis Manuel 10 Basit, Bolis 10 Boureanu, Maria-Magdalena 10 Cooper, Shane 10 Cui, Junzhi 10 Rautian, Nadegda Aleksandrovna 10 Shumilova, Vladlena Valerievna 10 Tarallo, Massimo 10 Valls Anglés, Cláudia 10 Vlasov, Viktor Valentinovich 9 Chechkin, Gregory A. 9 Fu, Yongqiang 9 Heidarkhani, Shapour 9 Lukkari, Teemu 9 Pankratov, Leonid S. 9 Sakbaev, Vsevolod Zhanovich 9 Skrypnik, Igor Igorievich 9 Slyusarchuk, Vasyl Yukhimovich 8 Ayazoglu (Mashiyev), Rabil A. 8 Dragičević, Davor 8 Günzler, Hans 8 Kovalevsky, Alexander Albertovich 8 Mel’nyk, Taras A. 8 N’Guérékata, Gaston Mandata 8 Ouaro, Stanislas 8 Smyshlyaev, Valery P. 8 Tachikawa, Atsushi 7 Abdulle, Assyr 7 Briane, Marc 7 Chiadò Piat, Valeria 7 Eleuteri, Michela 7 Gasiński, Leszek 7 He, Wenming 7 Mamedov, Farman Imran 7 Obaya, Rafael 7 Ourraoui, Anass 7 Panasenko, Grigory P. 7 Pucci, Patrizia 7 Sango, Mamadou 7 Spitkovsky, Ilya M. 7 Xu, Qiang 6 Bögelein, Verena 6 Caraballo Garrido, Tomás 6 Chepyzhov, Vladimir V. 6 Chlebicka, Iwona 6 Colombo, Maria 6 De Filippis, Cristiana 6 Diening, Lars 6 Gilbert, Robert Pertsch 6 Guo, Yunrui 6 Kim, Yunho 6 Kokilashvili, Vakhtang Mikhailovich 6 Leonetti, Francesco 6 Leugering, Günter 6 Lipton, Robert P. 6 Lukkassen, Dag 6 Meshkova, Yuliya Mikhaĭlovna 6 Messaoudi, Salim A. 6 Milton, Graeme Walter 6 Naito, Toshiki 6 Nesi, Vincenzo 6 Niu, Weisheng ...and 1,701 more Authors
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#### Cited in 310 Serials

 151 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 137 Journal of Mathematical Analysis and Applications 106 Journal of Mathematical Sciences (New York) 94 Journal of Differential Equations 56 Mathematical Notes 34 Applicable Analysis 33 St. Petersburg Mathematical Journal 29 Ukrainian Mathematical Journal 29 Journal of Functional Analysis 26 Annali di Matematica Pura ed Applicata. Serie Quarta 26 Functional Analysis and its Applications 25 Calculus of Variations and Partial Differential Equations 25 Boundary Value Problems 23 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 23 Doklady Mathematics 22 Archive for Rational Mechanics and Analysis 22 Computers & Mathematics with Applications 22 Applied Mathematics and Computation 21 SIAM Journal on Mathematical Analysis 21 Complex Variables and Elliptic Equations 20 Differential Equations 20 Proceedings of the Steklov Institute of Mathematics 18 Journal de Mathématiques Pures et Appliquées. Neuvième Série 17 Mathematical Methods in the Applied Sciences 17 Siberian Mathematical Journal 17 Nonlinear Analysis. Real World Applications 16 Multiscale Modeling & Simulation 15 ZAMP. Zeitschrift für angewandte Mathematik und Physik 15 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 15 Abstract and Applied Analysis 14 Computer Methods in Applied Mechanics and Engineering 14 Journal of Computational and Applied Mathematics 14 Proceedings of the American Mathematical Society 13 NoDEA. Nonlinear Differential Equations and Applications 12 International Journal of Engineering Science 12 Journal of Computational Physics 12 Communications on Pure and Applied Analysis 12 Advances in Nonlinear Analysis 10 Journal of the Mechanics and Physics of Solids 10 Journal of Dynamics and Differential Equations 10 Journal of Inequalities and Applications 9 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 9 Russian Mathematics 9 Journal of Difference Equations and Applications 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Mediterranean Journal of Mathematics 9 Discrete and Continuous Dynamical Systems. Series S 9 Nonlinear Analysis. Theory, Methods & Applications 8 Communications in Mathematical Physics 8 Integral Equations and Operator Theory 8 Manuscripta Mathematica 8 Mathematische Nachrichten 8 Mathematical and Computer Modelling 8 Russian Journal of Mathematical Physics 8 Revista Matemática Complutense 8 Discrete and Continuous Dynamical Systems. Series B 8 Advances in Difference Equations 7 Journal of Applied Mathematics and Mechanics 7 Journal of Mathematical Physics 7 Transactions of the American Mathematical Society 7 Acta Applicandae Mathematicae 7 Probability Theory and Related Fields 7 Applied Mathematics Letters 7 Opuscula Mathematica 7 Discrete and Continuous Dynamical Systems 7 Acta Mathematica Sinica. English Series 7 Boletim da Sociedade Paranaense de Matemática. Terceira Série 6 Nonlinearity 6 Journal of Optimization Theory and Applications 6 Journal of Soviet Mathematics 6 Semigroup Forum 6 Transactions of the Moscow Mathematical Society 6 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 6 Stochastic Processes and their Applications 6 Journal of Function Spaces 5 Applied Numerical Mathematics 5 Applications of Mathematics 5 Electronic Journal of Differential Equations (EJDE) 5 Differential Equations and Dynamical Systems 5 Networks and Heterogeneous Media 4 Bulletin of the Australian Mathematical Society 4 Journal d’Analyse Mathématique 4 Rocky Mountain Journal of Mathematics 4 Wave Motion 4 Mathematische Annalen 4 Mathematics and Computers in Simulation 4 Numerical Functional Analysis and Optimization 4 Ricerche di Matematica 4 Zeitschrift für Analysis und ihre Anwendungen 4 Chinese Annals of Mathematics. Series B 4 Computational Mathematics and Mathematical Physics 4 Communications in Partial Differential Equations 4 Journal of Elasticity 4 Applied and Computational Harmonic Analysis 4 Bulletin des Sciences Mathématiques 4 Sbornik: Mathematics 4 Journal of Applied Mathematics 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Communications in Mathematical Analysis 4 Advances in Calculus of Variations ...and 210 more Serials
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#### Cited in 49 Fields

 1,261 Partial differential equations (35-XX) 283 Ordinary differential equations (34-XX) 241 Operator theory (47-XX) 206 Mechanics of deformable solids (74-XX) 204 Calculus of variations and optimal control; optimization (49-XX) 185 Functional analysis (46-XX) 140 Fluid mechanics (76-XX) 87 Probability theory and stochastic processes (60-XX) 81 Numerical analysis (65-XX) 77 Global analysis, analysis on manifolds (58-XX) 72 Dynamical systems and ergodic theory (37-XX) 71 Harmonic analysis on Euclidean spaces (42-XX) 44 Abstract harmonic analysis (43-XX) 43 Optics, electromagnetic theory (78-XX) 40 Difference and functional equations (39-XX) 37 Integral equations (45-XX) 28 Statistical mechanics, structure of matter (82-XX) 26 Real functions (26-XX) 23 Classical thermodynamics, heat transfer (80-XX) 23 Systems theory; control (93-XX) 22 Biology and other natural sciences (92-XX) 19 Potential theory (31-XX) 13 General topology (54-XX) 13 Quantum theory (81-XX) 10 Measure and integration (28-XX) 10 Functions of a complex variable (30-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 5 Approximations and expansions (41-XX) 5 Integral transforms, operational calculus (44-XX) 4 General and overarching topics; collections (00-XX) 4 Number theory (11-XX) 4 Topological groups, Lie groups (22-XX) 4 Mechanics of particles and systems (70-XX) 3 Geophysics (86-XX) 2 History and biography (01-XX) 2 Special functions (33-XX) 2 Differential geometry (53-XX) 2 Statistics (62-XX) 2 Operations research, mathematical programming (90-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Sequences, series, summability (40-XX) 1 Computer science (68-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)

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