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

We consider a generalized steady Stokes system with discontinuouscoefficients in a nonsmooth domain when the inhomogeneous term belongs to aweighted $L^q$ space for $2<q<\infty$. We prove the global weighted$L^q$-estimates for the gradient of the weak solution and an associatedpressure under the assumptions that the coefficients have small BMO (boundedmean oscillation) semi-norms and the domain is sufficiently flat in theReifenberg sense. On the other hand, a given weight is assumed to belong to aMuckenhoupt class. Our result generalizes the global $W^{1.q}$ estimate ofCalder\'{o}n-Zygmund with respect to the Lebesgue measure for the Stokes systemin a Lipschitz domain.

Weighted estimates for generalized steady Stokes systems in nonsmooth domains