Calculus of Variations and Geometric Measure Theory

G. Cupini - P. Marcellini - E. Mascolo - A. Passarelli di Napoli

Lipschitz regularity for degenerate elliptic integrals with $p,q$-growth

created by passarell on 04 Jan 2021



Inserted: 4 jan 2021
Last Updated: 4 jan 2021

Year: 2021


We establish the local Lipschitz continuity and the higher differentiability of vector-valued local minimizers of a class of energy integrals of the Calculus of Variations. The main novelty is that we deal with possibly degenerate energy densities with respect to the $x-$variable.

Keywords: Nonstandard growth conditions, lipschitz continuity, $p,q$-growth, Degenerate ellipticity