A pointwise characterisation of the PDE system of vectorial calculus of variations in <i>L</i><sup>โ</sup>
A pointwise characterisation of the PDE system of vectorial calculus of variations in <i>L</i><sup>โ</sup>
Abstract Let n , $N \in {\open N}$ with $\Omega \subseteq {\open R}^n$ open. Given ${\rm H} \in C^2(\Omega \times {\open R}^N \times {\open R}^{Nn})$ , we consider the functional 1 $${\rm E}_\infty (u,{\rm {\cal O}})\, : = \, \mathop {{\rm ess}\,\sup}\limits_{\rm {\cal O}} {\rm H}(\cdot, u,{\rm D}u),\quad u\in W_{{\rm โฆ