Gradient estimates for singular $p$-Laplace type equations with measure data
Gradient estimates for singular $p$-Laplace type equations with measure data
复制标题
具有测量数据的奇异$p$-拉普拉斯型方程的梯度估计
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Hanye Zhu
中科院分区：
文献类型：
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作者：
Hongjie Dong;Hanye Zhu
研究了一类具测度的奇异拟线性椭圆型方程解的内部和整体梯度估计，其原型是p-拉普拉斯方程-Delta_p u=mu$，其中pin（1，2）$.当$pin IG（2-frac 1 n，2IG）$和$pin IG（压裂{3 n-2}{2n-1}，2-压裂{1}{n}[9]和[22]中分别研究了IG]$。在本文中，我们改进了[22]中的结果，并解决了当$pin IG（1，frac{3n-2}{2n-1}IG]$。内部和整体连续模估计的梯度的解决方案也建立。
We are concerned with interior and global gradient estimates for solutions to a class of singular quasilinear elliptic equations with measure data, whose prototype is given by the $p$-Laplace equation $-Delta_p u=mu$ with $pin (1,2)$. The cases when $pin ig(2-frac 1 n,2ig)$ and $pin ig(frac{3n-2}{2n-1},2-frac{1}{n}ig]$ were studied in [9] and [22], respectively. In this paper, we improve the results in [22] and address the open case when $pin ig(1,frac{3n-2}{2n-1}ig]$. Interior and global modulus of continuity estimates of the gradients of solutions are also established.