|
This article is cited in 18 scientific papers (total in 18 papers)
Brief communications
On homogenization for non-self-adjoint locally periodic elliptic operators
N. N. Senik St. Petersburg State University, St. Petersburg, Russia
Abstract:
In this note we consider the homogenization problem for a matrix locally periodic elliptic operator on Rd of the form Aε=−divA(x,x/ε)∇. The function A is assumed to be Hölder continuous with exponent s∈[0,1] in the “slow” variable and bounded in the “fast” variable. We construct approximations for (Aε−μ)−1, including one with a corrector, and for (−Δ)s/2(Aε−μ)−1 in the operator norm on L2(Rd)n. For s≠0, we also give estimates of the rates of approximation.
Keywords:
homogenization, operator error estimates, locally periodic operators, effective operator, corrector.
Received: 23.01.2017
Citation:
N. N. Senik, “On homogenization for non-self-adjoint locally periodic elliptic operators”, Funktsional. Anal. i Prilozhen., 51:2 (2017), 92–96; Funct. Anal. Appl., 51:2 (2017), 152–156
Linking options:
https://www.mathnet.ru/eng/faa3457https://doi.org/10.4213/faa3457 https://www.mathnet.ru/eng/faa/v51/i2/p92
|
Statistics & downloads: |
Abstract page: | 437 | Full-text PDF : | 71 | References: | 68 | First page: | 17 |
|