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

Lukas Koch

We prove global $W^{1,q}(\Omega ,{\mathbb{R}}^N)$-regularity for minimisers of $\mathcal{F}(u)={\int }_{\Omega }F(x,\mathrm{D}u)\mathrm{d}x$ satisfying $u\ge \psi$ for a given Sobolev obstacle $\psi$. $W…