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

Abstract

A partial regularity theorem is presented for minimisers of $k$th-order functionals subject to a quasiconvexity and general growth condition. We will assume a natural growth condition governed by an $N$-function satisfying the ${\Delta }_2$ and ${\nabla }_2$ 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.

arXiv comment22 pages, accepted version

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