The Stokes Operator in Weighted $L^{q}$-Spaces I: Weighted Estimates for the Stokes Resolvent Problem in a Half Space
The Stokes Operator in Weighted $L^{q}$-Spaces I: Weighted Estimates for the Stokes Resolvent Problem in a Half Space
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加权 $L^{q}$-空间中的斯托克斯算子 I：半空间中斯托克斯求解问题的加权估计
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发表时间：
2003
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通讯作者：
Andreas Fröhlich
中科院分区：
文献类型：
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作者：
Andreas Fröhlich
抽象的。本文给出了半空间中Stokes预解式系的Muckenhoupt类权的加权L^{q}-估计，在此基础上，我们将在第二部分中得到加权L ^{q}-空间中Stokes算子在半空间和有界区域上的极大L ^{p}-正则性的新方法.我们强调，我们的结果保持一般Muckenhoupt重量。特别地，权重可能趋于零或在域的边界处变得奇异。
Abstract. In this paper we derive weighted $L^{q}$-estimates for the Stokes resolvent system in the half space for weights of Muckenhoupt class, on which a new approach to maximal $L^{p}$-regularity of the Stokes operator for the half space and a bounded domain in weighted $L^{q}$-spaces in the forthcoming part II is based. We stress that our results hold for general Muckenhoupt weights. In particular, the weights may tend to zero or become singular at the boundary of the domain.