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Corpus ID: 225102909

Global higher integrability for minimisers of convex functionals with (p,q)-growth

@article{Koch2020GlobalHI,
title={Global higher integrability for minimisers of convex functionals with (p,q)-growth},
author={Lukas Koch},
journal={arXiv: Analysis of PDEs},
year={2020}
}

We prove global $W^{1,q}(\Omega,\mathbb{R}^m)$-regularity for minimisers of convex functionals of the form $\mathscr{F}(u)=\int_\Omega F(x,Du)\mathrm{d} x$. $W^{1,q}(\Omega,\mathbb{R}^m)$ regularity is also proven for minimisers of the associated relaxed functional. Our main assumptions on $F(x,z)$ are a uniform $\alpha$-Holder continuity assumption in $x$ and controlled $(p,q)$-growth conditions in $z$ with $q<\frac{(n+\alpha)p}{n}$.