Local and global pointwise gradient estimates are obtained for solutions to the quasilinear elliptic equation with measure data $-\operatorname{div}(A(x,\nabla u))=\mu$ in a bounded and possibly nonsmooth domain $\Omega$ in $\mathbb{R}^n$. Here $\operatorname{div}(A(x,\nabla u))$ is modeled after the $p$-Laplacian. Our results extend earlier known results to the singular case in which $\frac{3n-2}{2n-1}

中文翻译：

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一类具有测量数据的奇异拟线性方程的逐点梯度估计

局部和全局逐点梯度估计是针对准线性椭圆方程的解获得的，其测量数据为 $-\operatorname{div}(A(x,\nabla u))=\mu$ 在有界且可能不光滑的域 $\Omega$在 $\mathbb{R}^n$ 中。这里 $\operatorname{div}(A(x,\nabla u))$ 是根据 $p$-Laplacian 建模的。我们的结果将早期已知的结果扩展到奇异情况，其中 $\frac{3n-2}{2n-1}