Calculus of Variations and Geometric Measure Theory
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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

[BibTeX]

Accepted Paper

Inserted: 14 apr 2016
Last Updated: 2 aug 2016

Journal: Nonlinear Anal.
Pages: 32
Year: 2016
Notes:

Dedicated to Nicola Fusco with gratitude and friendship on the occasion of his birthday


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.

Keywords: Degenerate elliptic equations, Anisotropic problems, Besov-Nikol'skii spaces


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