Absolutely minimising generalised solutions to the equations of vectorial calculus of variations in $$L^\infty $$ L โ
Absolutely minimising generalised solutions to the equations of vectorial calculus of variations in $$L^\infty $$ L โ
Consider the supremal functional 1 $$\begin{aligned} E_\infty (u,A) := \Vert \mathscr {L}(\cdot ,u,\mathrm {D}u)\Vert _{L^\infty (A)},\quad A\subseteq \Omega , \end{aligned}$$ applied to $$W^{1,\infty }$$ maps $$u:\Omega \subseteq \mathbb {R}\longrightarrow \mathbb {R}^N$$ , $$N\ge 1$$ . Under certain assumptions on $$\mathscr {L}$$ , we prove for any given boundary data the โฆ