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A partial regularity theorem is presented for minimisers of $k$th-orderfunctionals subject to a quasiconvexity and general growth condition. We willassume a natural growth condition governed by an $N$-function satisfying the$\Delta_2$ and $\nabla_2$ conditions, assuming no quantitative estimates on thesecond derivative of the integrand; this is new even in the $k = 1$ case. Theseresults will also be extended to the case of strong local minimisers.

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