论文标题
奇异p-Laplace系统的加权Orlicz Orlicz梯度估计值
Weighted Orlicz gradient estimates for the class of singular p-Laplace system
论文作者
论文摘要
令$ n \ in \ {2，3，4，\ ldots \} $，$ n \ in \ {1，2，3，\ ldots \} $和$ p \ in \ big（1，2- \ frac {1} {n} {n} {n} {n} {n} \ big] $。 \ frac {np} {n-p} <β'<\ frac {n} {n（2-p）-1} \]和$ f \ in l^β（\ mathbb r^n; \ mathbb r^n）in u = - \ operatotorname {div} \ big（| du |^{p-2} du \ big）= f \ quad in \ quad \ mathbb r^n。
Let $n \in \{2, 3, 4, \ldots\}$, $N \in \{1, 2, 3, \ldots\}$ and $p \in \big(1, 2-\frac{1}{n}\big]$. Let $β\in (1,\infty)$ be such that \[ \frac{np}{n-p}<β'<\frac{n}{n(2-p)-1} \] and $f \in L^β(\mathbb R^n;\mathbb R^N)$. Consider the $p$-Laplace system \[ -Δ_p u=-\operatorname{div}\big(|Du|^{p-2}Du\big)=f \quad in \quad \mathbb R^n. \] We obtain a weighted gradient estimate for distributional solutions of this system.
