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

TL;DR

This paper establishes a partial regularity theorem for minimizers of higher-order quasiconvex functionals with natural Orlicz growth, extending previous results to more general growth conditions without requiring second derivative estimates.

Contribution

It introduces a novel partial regularity result for higher-order quasiconvex minimizers under natural Orlicz growth, even when second derivative estimates are unavailable.

Findings

Partial regularity theorem for higher-order quasiconvex minimizers.

Extension to strong local minimizers.

Results hold under general Orlicz growth conditions without second derivative estimates.

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.