论文标题
具有非标准增长的变异积分的较高可集成性
Higher integrability for variational integrals with non-standard growth
论文作者
论文摘要
我们考虑$ \ mathcal f [u]的自主积分功能：= \int_Ωf（d u）\，dx $，带有$ u：u：ω\ to \ mathbb r^n $ $ n $ $ n $ n \ geq1 $，convex Integrand $ f $ f $ f $ f $满足（P，Q）$ - 增长条件。我们为$ \ Mathcal f $的最小化器建立了更高的梯度集成性和部分规律性，假设$ \ frac {q} p <1+ \ frac2 {n-1} $，$ n \ geq3 $。这改善了较早的结果在更限制的假设$ \ frac {q} p <1+ \ frac2 {n} $中有效。
We consider autonomous integral functionals of the form $\mathcal F[u]:=\int_Ωf(D u)\,dx$ with $u:Ω\to\mathbb R^N$ $N\geq1$, where the convex integrand $f$ satisfies controlled $(p,q)$-growth conditions. We establish higher gradient integrability and partial regularity for minimizers of $\mathcal F$ assuming $\frac{q}p<1+\frac2{n-1}$, $n\geq3$. This improves earlier results valid under the more restrictive assumption $\frac{q}p<1+\frac2{n}$.
