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arXiv · 2111.14740

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

Christopher Irving
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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.

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Christopher Irving. 2021-11-29. Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth. https://doi.org/10.1007/s10231-025-01547-2

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