Solutions of vectorial Hamilton-Jacobi equations are rank-one absolute minimisers in L∞

Katzourakis, N. (2019) Solutions of vectorial Hamilton-Jacobi equations are rank-one absolute minimisers in L∞. Advances in Nonlinear Analysis, 8 (1). pp. 508-516. ISSN 2191-950X doi: 10.1515/anona-2016-0164

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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/69970
Identification Number/DOI	10.1515/anona-2016-0164
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Walter de Gruyter
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