Vasilii Vasil'evich Zhikov

Korn inequalities on thin periodic structures

We prove Korn-type inequalities for thin periodic structures of period

On an extension of the method of two-scale convergence and its applications

\varepsilon

Weighted Sobolev spaces

and thickness

Connectedness and homogenization. Examples of fractal conductivity

\varepsilon h(\varepsilon)

Усреднение задач теории упругости на сингулярных структурах@@@Homogenization of elasticity problems on singular structures

, where

К проблеме предельного перехода в дивергентных неравномерно эллиптических уравнениях@@@To the Problem of Passage to the Limit in Divergent Nonuniformly Elliptic Equations

h(\varepsilon)\to 0

Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent

as

Homogenization for elasticity problems on periodic networks of critical thickness

\varepsilon\to 0

К технике предельного перехода в нелинейных эллиптических уравнениях@@@On the Technique for Passing to the Limit in Nonlinear Elliptic Equations

, among which there are plane grids, spatial rod and box structures. These inequalities are important in homogenization of corresponding elasticity problems.