## P. Baroni - T. Kuusi - G. Mingione

# Borderline gradient continuity of minima

created by baroni on 13 Feb 2018

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BibTeX]

*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

**Abstract:**

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.

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