Calculus of Variations and Geometric Measure Theory

P. Baroni - T. Kuusi - G. Mingione

Borderline gradient continuity of minima

created by baroni on 13 Feb 2018


Published Paper

Inserted: 13 feb 2018
Last Updated: 13 feb 2018

Journal: J. Fixed Point Theory Appl
Volume: 15
Number: 2
Pages: 537-575
Year: 2014
Doi: 10.1007/s11784-014-0188-x


The gradient of any local minimiser of functionals of the type \[ w \mapsto \int_\Omega f(x,w,Dw)\,dx+\int_\Omega w\mu\,dx, \] 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.