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

TL;DR

This paper proves partial regularity for minimizers of elliptic functionals with Orlicz growth, extending regularity results to cases like $L ext{log} L$-growth and using reduction techniques inspired by prior work.

Contribution

It establishes partial regularity results for $ ext{A}$-quasiconvex functionals with Orlicz growth, including $L ext{log} L$-growth, using a reduction approach to full gradient regularity.

Findings

Partial regularity results for elliptic functionals with Orlicz growth.

Extension to $L ext{log} L$-growth scenarios.

Reduction to full gradient regularity cases.

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 $\Delta_{2}\cap\nabla_{2}$-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.