  We prove that minimizers of the $L^{d}$-norm of the Hessian in the unit ball
of $\mathbb{R}^d$ are locally of class $C^{1,\alpha}$. Our findings extend
previous results on Hessian-dependent functionals to the borderline case and
resonate with the H\"older regularity theory available for elliptic equations
in double-divergence form.
