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

We show that for any regular bounded domain $\Omega\subseteq \mathbb R^n$,$n=2,3$, there exist infinitely many global diffeomorphisms equal to theidentity on $\partial \Omega$ which solve the Eikonal equation. We also provideexplicit examples of such maps on annular domains. This implies that the$\infty$-Laplace system arising in vectorial Calculus of Variations in$L^\infty$ does not suffice to characterise either limits of $p$-Harmonic mapsas $p\to \infty$, or absolute minimisers in the sense of Aronsson.

Counterexamples in Calculus of Variations in $L^\infty$ through the vectorial Eikonal equation