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

TL;DR

This paper establishes higher differentiability and Lipschitz regularity of local minimizers for a class of degenerate anisotropic functionals, expanding understanding of their regularity properties.

Contribution

It proves higher differentiability for general degenerate anisotropic functionals and Lipschitz continuity in two dimensions without anisotropy restrictions.

Findings

Higher differentiability of minimizers under superquadratic growth

Lipschitz regularity in 2D for model functionals

No anisotropy restrictions in 2D case

Abstract

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.