Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 69, pp. 1-19

Title: Holder continuity for vector-valued minimizers  of quadratic functionals 
       
Authors: Josef Danecek (VSB - Technical Univ. of Ostrava, FEECS, Czech Republic)
         Eugen Viszus (Comenius Univ.,  Mlynska dolina, Slovak Republic)

Abstract:
 In this article we give a sufficient condition
 for interior everywhere Holder continuity of weak minimizers
 of a class of quadratic functionals
 with coefficients $A_{ij}^{\alpha\beta}(\cdot,u)$ belonging
 to the VMO-class, uniformly with respect to $u\in\mathbb{R}^{N}$, and
 continuous with respect to u.
 The condition is global. It is typical for the
 functionals belonging to the class that the continuity moduli of their
 coefficients become  slowly growing sufficiently far from zero. Some
 features of the main result  are illustrated by examples.
 
Submitted April 4, 2019. Published July 02, 2020.
Math Subject Classifications: 35J60.
Key Words: Quadratic functionals; minimizers; regularity; Morrey spaces.