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

For solutions of ${\rm div}\,(DF(Du))=f$ we show that the quasiconformalityof $z\mapsto DF(z)$ is the key property leading to the Sobolev regularity ofthe stress field $DF(Du)$, in relation with the summability of $f$. This classof nonlinearities encodes in a general way the notion of uniform ellipticityand encompasses all known instances where the stress field is known to beSobolev regular. We provide examples showing the optimality of this assumptionand present three applications: the study of the strong locality of theoperator ${\rm div}\,(DF(Du))$, a nonlinear Cordes condition for equations indivergence form, and some partial results on the $C^{p'}$-conjecture.

A general notion of uniform ellipticity and the regularity of the stress field for elliptic equations in divergence form