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arXiv · 1409.8122

Borderline gradient continuity of minima

Paolo Baroni·Tuomo Kuusi·Giuseppe Mingione
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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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Paolo Baroni, Tuomo Kuusi, Giuseppe Mingione. 2014-09-29. Borderline gradient continuity of minima. https://arxiv.org/abs/1409.8122

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