Abstract/Summary

Given the supremal functional E∞(u,Ω′)=esssupΩ′H(⋅,Du)E∞(u,Ω′)=esssupΩ′H(⋅,Du) defined on W1,∞loc(Ω,RN)Wloc1,∞(Ω,RN), Ω′⋐Ω⊆RnΩ′⋐Ω⊆Rn, 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 equation H(⋅,Du)=cH(⋅,Du)=c are rank-one Absolute Minimisers if they are C1C1. Our minimality notion is a generalisation of the classical L∞L∞ 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.