Improved regularity for a Hessian-dependent functional

We prove that minimizers of the L d L^d -norm of the Hessian in the unit ball of R d Rᵈ are locally of class C 1, α C^1,. 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.