Operator estimates in homogenization theory. (English. Russian original) Zbl 1354.35028
Russ. Math. Surv. 71, No. 3, 417-511 (2016); translation from Usp. Mat. Nauk 71, No. 3, 27-122 (2016).
The authors present a systematic treatment of two main methods used in operator estimates, namely the shift and the spectral method. The context where the two methods are described includes homogenization problems in the standard form, in perforated domains, unbounded diffusion matrix, non-self adjoint evolution equations and higher order elliptic operators.
Reviewer: Marius Ghergu (Dublin)
MSC:
35J15 | Second-order elliptic equations |
35K15 | Initial value problems for second-order parabolic equations |
35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
35J30 | Higher-order elliptic equations |