Abstract/Summary

For H ∈ C 2 ( R N × n ) and u : Ω ⊆ R n ⟶ R N , consider the system A ∞ u := ( H P ⊗ H P + H [ H P ] ⊥ H P P ) ( D u ) : D 2 u = 0. 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 W 1 , ∞ -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 .