$\mathscr{A}$-Quasiconvexity and Partial Regularity

TL;DR

This paper proves a novel partial regularity result for local minima of strongly $\

Contribution

It introduces the first partial regularity theorem for $\

Findings

Partial regularity established for local minima of $\

Results apply to trace-free symmetric gradient, exterior derivative, div-curl operators.

Reduces complex $\

Abstract

We establish the first partial regularity result for local minima of strongly $\mathscr{A}$-quasiconvex integrals in the case where the differential operator $\mathscr{A}$ possesses an elliptic potential $\mathbb{A}$. As the main ingredient, the proof works by reduction to the partial regularity for full gradient functionals. Specialising to particular differential operators, the results in this paper thereby equally yield novel partial regularity theorems in the cases of the trace-free symmetric gradient, the exterior derivative or the div-curl-operator.