Calculus of Variations and Geometric Measure Theory

L. Brasco - C. Leone - G. Pisante - A. Verde

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

created by brasco on 14 Apr 2016
modified on 02 Aug 2016


Accepted Paper

Inserted: 14 apr 2016
Last Updated: 2 aug 2016

Journal: Nonlinear Anal.
Pages: 32
Year: 2016

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