Existence of 1D vectorial Absolute Minimisers in $L^{\infty }$ under minimal assumptions

Hussien Abugirda, Nikos Katzourakis

We prove the existence of vectorial Absolute Minimisers in the sense of Aronsson to the supremal functional $E_{\infty }(u,{\Omega }^{\prime })=\Vert \mathcal{L}(\cdot ,u,Du){\Vert }_{L^{\infty }({\Omega }^{\prime })}$, $Ω'\Subs…