Inserted: 14 apr 2016
Last Updated: 2 aug 2016
Journal: Nonlinear Anal.
Dedicated to Nicola Fusco with gratitude and friendship on the occasion of his birthday
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.
Keywords: Degenerate elliptic equations, Anisotropic problems, Besov-Nikol'skii spaces