Differentiability for Bounded Minimizers of Some Anisotropic Integrals

We prove the existence of second weak derivatives for bounded minimizers u: Rn RNof the integral H Ž Du 2 Dnu q.dx, when 2 q 2Žn 1. Žn 3., n 4. This allows us to improve on the Hausdorff dimension of the singular set of u.