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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Fix strictly increasing right continuous functions with left limits $W_i:\bbR \to \bb R$, $i=1,...,d$, and let $W(x) = \sum_{i=1}^d W_i(x_i)$ for $x\in\bbR^d$. We construct the $W$-Sobolev spaces, which consist of functions $f$having weak generalized gradients $\nabla_W f = (\partial_{W_1}f,...,\partial_{W_d} f)$. Several properties, that are analogous to classicalresults on Sobolev spaces, are obtained. $W$-generalized elliptic and parabolicequations are also established, along with results on existence and uniquenessof weak solutions of such equations. Homogenization results of suitable randomoperators are investigated. Finally, as an application of all the theorydeveloped, we prove a hydrodynamic limit for gradient processes withconductances (induced by $W$) in random environments.

$W$-Sobolev spaces: Theory, Homogenization and Applications