  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.
