Partial regularity for $\mathbb{A}$-quasiconvex functionals with Orlicz growth

Abstract

We establish partial regularity results for minimizers of a class of functionals depending on differential expressions based on elliptic operators. Specifically, we focus on functionals of Orlicz growth with a natural strong quasiconvexity property. In doing so, we consider both $Δ_{2}\cap\nabla_{2}$-Orlicz growth scenarios and, as a limiting case, $L \log L$-growth. Inspired by Conti & Gmeineder (J Calc Var, 61:215, 2022), the proofs of our main results are accomplished by reduction to the case of full gradient partial regularity results.