Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth
Christopher Irving · Annali di Matematica Pura ed Applicata (1923 -) · 2025
Abstract A partial regularity theorem is presented for minimisers of $$k^{\textrm{th}}$$ 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 $$\Delta _2$$ Δ 2 and $$ abla _2$$ ∇ 2 conditions, assuming no quantitative estimates on the second derivative of the integrand; this is new even in the $$k=1$$ k = 1 case. These results will also be extended to the case of strong local minimisers.