D-solutions to the system of vectorial calculus of variations in L∞via the singular value problem

For H ∈ C2(ℝN×n) and u: Ω ⊆ Rn→ RN, consider the system A∞u:= (HP⊗ HP+ H[HP]⊥HPP) (Du): D2u = 0. (1) We construct D-solutions to the Dirichlet problem for (1), an apt notion of generalised solutions recently proposed for fully nonlinear systems. Our D-solutions are W1,∞-submersions and are obtained without any convexity hypotheses for H, through a result of independent interest involving existence of strong solutions to the singular value problem for general dimensions n ≠ N.