Preprint

Inserted: 7 jun 2026
Last Updated: 7 jun 2026

Year: 2026

Abstract:

We show that vectorial absolute minimisers of higher order $L^\infty$ variational problems satisfy an energy maximum principle. This property is only necessary for absolute minimisers, while it characterises a suitable weaker notion of absolute minimality involving compactly supported variations. Further, with different methods, we prove a gradient maximum principle for $p$-harmonic maps.

Keywords: Vectorial Calculus of Variations in $L^\infty$, higher order problems, Absolute Minimisers, Maximum Principle

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• MaxPr_strong_rad.pdf