Geodesic
Approximation of resolvents in homogenization of fourth-order elliptic operators
Sbornik. Mathematics, Tome 212 (2021) no. 1, pp. 111-134

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the homogenization of a fourth-order divergent elliptic operator $A_\varepsilon$ with rapidly oscillating $\varepsilon$-periodic coefficients, where $\varepsilon$ is a small parameter. The homogenized operator $A_0$ is of the same type and has constant coefficients. We apply Zhikov's shift method to obtain an estimate in the $(L^2\to L^2)$-operator norm of order $\varepsilon^2$ for the difference of the resolvents $(A_\varepsilon+1)^{-1}$ and $(A_0+1)^{-1}$. Bibliography: 25 titles.
Keywords: approximation of resolvents, operator estimate of the homogenization error, corrector, shift method, fourth-order elliptic operator. 
@article{SM_2021_212_1_a4,
     author = {S. E. Pastukhova},
     title = {Approximation of resolvents in homogenization of fourth-order elliptic operators},
     journal = {Sbornik. Mathematics},
     pages = {111--134},
     publisher = {mathdoc},
     volume = {212},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2021_212_1_a4/}
}
TY  - JOUR
AU  - S. E. Pastukhova
TI  - Approximation of resolvents in homogenization of fourth-order elliptic operators
JO  - Sbornik. Mathematics
PY  - 2021
SP  - 111
EP  - 134
VL  - 212
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2021_212_1_a4/
LA  - en
ID  - SM_2021_212_1_a4
ER  - 
%0 Journal Article
%A S. E. Pastukhova
%T Approximation of resolvents in homogenization of fourth-order elliptic operators
%J Sbornik. Mathematics
%D 2021
%P 111-134
%V 212
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2021_212_1_a4/
%G en
%F SM_2021_212_1_a4
S. E. Pastukhova. Approximation of resolvents in homogenization of fourth-order elliptic operators. Sbornik. Mathematics, Tome 212 (2021) no. 1, pp. 111-134. http://geodesic.mathdoc.fr/item/SM_2021_212_1_a4/