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. 
Lorenzo Brasco, Chiara Leone, Giovanni Pisante and Anna Verde
math.AP