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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This article is about the $\mathbb{Z}^d$-periodic Green function $G_n(x,y)$of the multiscale elliptic operator $Lu=-{\rm div}\left( A(n\cdot) \cdot \nablau \right)$, where $A(x)$ is a $\mathbb{Z}^d$-periodic, coercive, and H\"oldercontinuous matrix, and $n$ is a large integer. We prove here pointwiseestimates on $G_n(x,y)$, $\nabla_x G_n(x,y)$, $\nabla_y G_n(x,y)$ and $\nabla_x\nabla_y G_n(x,y)$ in dimensions $d \geq 2$. Moreover, we derive an explicitdecomposition of this Green function, which is of independent interest. Theseresults also apply for systems.

Decomposition and pointwise estimates of periodic Green functions of some elliptic equations with periodic oscillatory coefficients