# Borderline gradient continuity of minima

created by mingione on 04 Aug 2014
modified on 16 Jan 2015

[BibTeX]

Published Paper

Inserted: 4 aug 2014
Last Updated: 16 jan 2015

Journal: J. Fixed Point Theory Appl.
Volume: 15
Pages: 537--575
Year: 2014
Notes:

appears in Haim Brezis festschrift

Abstract:

The gradient of any local minimizer of functionals of the type $w \to \int_{\Omega} f(x,w,Dw)\, dx+\int_{\Omega} w\mu\, dx,$ where $f$ has $p$-growth, $p>1$, and $\Omega \subset \mathbb R^n$, is continuous provided the optimal Lorentz space condition $\mu \in L(n,1)$ is satisfied and $x\to f(x, \cdot)$ is suitably Dini-continuous.