论文标题
使用（P，Q）增长的凸功能的最小值的全局较高的集成性
Global higher integrability for minimisers of convex functionals with (p,q)-growth
论文作者
论文摘要
我们证明全局$ w^{1，q}（ω，\ mathbb {r}^m）$ - 适用于表格$ \ mathscr {f}（f}（u）= \int_Ωf（x，x，x，x，du）\ mathrm {d} x $的最小值。 $ w^{1，q}（ω，\ mathbb {r}^m）$也可以证明适用于相关放松功能的最小化器。我们对$ f（x，z）$的主要假设是$ x $和受控$（p，q）$（p，q）$的均匀$α$-Hölder连续性假设，$ z $中的增长条件，$ q <\ frac {（n+α）p} p} p} {n} $。
We prove global $W^{1,q}(Ω,\mathbb{R}^m)$-regularity for minimisers of convex functionals of the form $\mathscr{F}(u)=\int_ΩF(x,Du)\mathrm{d} x$. $W^{1,q}(Ω,\mathbb{R}^m)$ regularity is also proven for minimisers of the associated relaxed functional. Our main assumptions on $F(x,z)$ are a uniform $α$-Hölder continuity assumption in $x$ and controlled $(p,q)$-growth conditions in $z$ with $q<\frac{(n+α)p}{n}$.
