Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth

A partial regularity theorem is presented for minimisers of kth -order functionals subject to a quasiconvexity and general growth condition. We will assume a natural growth condition governed by an N-function satisfying the Δ2 and ∇2 conditions, assuming no quantitative estimates on the second derivative of the integrand; this is new even in the k=1 case. These results will also be extended to the case of strong local minimisers.