Weighted Orlicz gradient estimates for the class of singular p-Laplace system

Let $n\in \{2,3,4,\dots \}$, $N\in \{1,2,3,\dots \}$ and $p \in \big(1, 2-\frac{1}{n}\big]$\mathrm{.}Let$\beta \in (1,\infty)$ be such that $$\frac{np}{n-p}<{\beta }^{\mathrm{\prime }}<\frac{n}{n(2-p)-1}$$ and $f \in L^{\beta}(\mathbb R^n;\mathbb R^N)$\mathrm{.}Considerthe$p$-Laplace system $$-{\mathrm{\Delta }}_{p}u=-\mathrm{div}\left(\mathrm{\mid }Du{\mathrm{\mid }}^{p-2}Du\right)=fin{\mathbb{R}}^n\mathrm{.}$$ We obtain a weighted gradient estimate for distributional solutions of this system.