English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study and characterize the optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form. We obtain that the optimal rate of convergence is either $O(\varepsilon)$ or $O(\varepsilon^2)$ depending on the diffusion matrix $A$, source term $f$, and boundary data $g$. Moreover, we show that the set of diffusion matrices $A$ that give optimal rate $O(\varepsilon)$ is open and dense in the set of $C^2$ periodic, symmetric, and positive definite matrices, which means that generically, the optimal rate is $O(\varepsilon)$.

Remarks on optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form