  We prove the existence of vectorial Absolute Minimisers in the sense of
Aronsson to the supremal functional $E_\infty(u,\Omega') =
\|\mathscr{L}(\cdot,u,D u)\|_{L^\infty(\Omega')}$, $\Omega'\Subset \Omega$,
applied to $W^{1,\infty}$ maps $u:\Omega\subseteq \mathbb{R}\longrightarrow
\mathbb{R}^N$ with given boundary values. The assumptions on $\mathscr{L}($ are
minimal, improving earlier existence results previously established by
Barron-Jensen-Wang and by the second author.
