Nonlinear Potential Estimates for Generalized Stokes System
Nonlinear Potential Estimates for Generalized Stokes System
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DOI：
10.1007/s00009-022-02135-x
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发表时间：
2021-08
影响因子：
1.1
通讯作者：
Lingwei Ma;Zhenqiu Zhang;F. Zhou
中科院分区：
文献类型：
--
作者：
Lingwei Ma;Zhenqiu Zhang;F. Zhou
本文考虑具有p-增长和Dini-正则系数的广义平稳Stokes系统。本文的主要目的是利用平面上非齐次项的非线性Havin-Maz'ya-Wolff型势，对这类Stokes系统的剪切速率和相应的压力建立逐点估计。因此，得到了一个对称的梯度估计。此外，我们得到了潜在的估计弱解的Stokes系统没有额外的正则性假设的系数在高维空间。
In this paper, we consider the generalized stationary Stokes system withp-growth and Dini-regular coefficients. The main purpose is to establish pointwise estimates for the shear rate and the associated pressure to such Stokes system in terms of an unconventional nonlinear Havin–Maz’ya–Wolff type potential of the nonhomogeneous term in the plane. As a consequence, a symmetric gradientestimate is obtained. Moreover, we derive potential estimates for the weak solution to the Stokes system without additional regularity assumptions on the coefficients in higher dimensional space.