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

Homogenization of a scalar elliptic equation in a bounded domain with Neumanboundary condition is studied. Coefficients of the operator are oscillatingover two different groups of variables with different small periods$\varepsilon$ and $\delta=\delta(\varepsilon)$. We assume that${\delta}/{\varepsilon}$ tends to zero as $\varepsilon$ tends to zero. It isknown that the limit problem is obtained through reiterated homogenizationprocedure and corresponds to an elliptic equation with constant coefficients.The difference for resolvents of the initial and the limit problems isestimated in operator $(L^2\to L^2)$-norm. This estimate is of order$\tau=\tau(\varepsilon)$ which is the maximum of $\ve$ and${\delta}/{\varepsilon}$. We find also the approximation of the initialresolvent in operator $(L^2\to H^1)$-norm, it is of order $\sqrt{\tau}$.

On homogenization estimates in Neuman boundary value problem for an elliptic equation with multiscale coefficients