Holder continuity for vector-valued minimizers of quadratic functionals
Date
2020-07-02
Authors
Danecek, Josef
Viszus, Eugen
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we give a sufficient condition for interior everywhere Hölder continuity of weak minimizers of a class of quadratic functionals with coefficients Aαβ ij(‧, u) belonging to the VMO-class, uniformly with respect to u ∈ ℝN, 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.
Description
Keywords
Quadratic functionals, Minimizers, Regularity, Morrey spaces
Citation
Danecek, J., & Viszus, E. (2020). Holder continuity for vector-valued minimizers of quadratic functionals. <i>Electronic Journal of Differential Equations, 2020</i>(69), pp. 1-19.