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

Given the supremal functionalE∞⁢(u,Ω′)=ess⁢supΩ′⁡H⁢(⋅,D⁢u){E_{\infty}(u,\Omega^{\prime})=\operatornamewithlimits{ess\,sup}_{\Omega^{% \prime}}H(\,\cdot\,,\mathrm{D}u)}, defined onWloc1,∞⁢(Ω,ℝN){W^{1,\infty}_{\mathrm{loc}}(\Omega,\mathbb{R}^{N})}, withΩ′⋐Ω⊆ℝn{\Omega^{\prime}\Subset\Omega\subseteq\mathbb{R}^{n}}, we identify a class of vectorial rank-one absolute minimisers by proving a statement slightly stronger than the next claim: vectorial solutions of the Hamilton–Jacobi equationH⁢(⋅,D⁢u)=c{H(\,\cdot\,,\mathrm{D}u)=c}are rank-one absolute minimisers if they areC1{C^{1}}. Our minimality notion is a generalisation of the classicalL∞{L^{\infty}}variational principle of Aronsson to the vector case, and emerged in earlier work of the author. The assumptions are minimal, requiring only continuity and rank-one convexity of the level sets.

advances in nonlinear analysis

Solutions of vectorial Hamilton–Jacobi equations are rank-one absolute minimisers in                                                                                                    L                              ∞                                                                                                 L^{\infty}