Speciality:
01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
17.05.1970
E-mail: Keywords: homogenization of differential operators and nonlinear variational functionals; monotone operators.
Subject:
Nonlinear variational boundary value problems, in particular, the variational problems in perforated domains and the variational problems with degenerate integrands, was studied. The homogenization theorem was proved not using the classical extension technique of solutions in Sobolev spaces. Here the "strong connectedness" of the perforated domain was replaced by the usual connectedness. The homogenization theorem for nonlinear second-order monotone elliptic equations in perforated domains was proved. The homogenization properties for monotone elliptic operators on Euclidean space with measure was studied. The corresponding condition of p-connectedness was formulated and a new "measure approach", proposed by V. V. Zhikov was realised.
Main publications:
Zhikov V. V., Rychago M. E. Usrednenie ellipticheskikh uravnenii vtorogo poryadka v perforirovannykh oblastyakh // Izvestiya RAN, seriya matematicheskaya, 1997, t. 61, # 1, s. 69–88.
Rychago M. E. Ob usrednenii nekotorykh nelineinykh variatsionnykh zadach // Fundamentalnaya i prikladnaya matematika, 2000, t. 6, # 2.
