Sobolev and Lipschitz regularity for local minimizers of widely degenerate anisotropic functionals

We prove higher differentiability of bounded local minimizers to some widely degenerate functionals, verifying superquadratic anisotropic growth conditions. In the two dimensional case, we prove that local minimizers to a model functional are locally Lipschitz continuous functions, without any restriction on the anisotropy. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM