Improved regularity for a Hessian-dependent functional.

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 Hölder regularity theory available for elliptic equations in double-divergence form. [ABSTRACT FROM AUTHOR]