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

Let $E$ be an arbitrary subset of $\mathbb{R}^n$ (not necessarily bounded),and $f:E\to\mathbb{R}$, $G:E\to\mathbb{R}^n$ be functions. We provide necessaryand sufficient conditions for the $1$-jet $(f,G)$ to have an extension $(F,\nabla F)$ with $F:\mathbb{R}^n\to\mathbb{R}$ convex and of class $C^{1}$.Besides, if $G$ is bounded we can take $F$ so that $\textrm{Lip}(F)\lesssim\|G\|_{\infty}$. As an application we also solve a similar problem aboutfinding convex hypersurfaces of class $C^1$ with prescribed normals at thepoints of an arbitrary subset of $\mathbb{R}^n$.

Global geometry and $C^1$ convex extensions of $1$-jets