Weighted resolvent estimates for the spatially periodic Stokes equations

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• 作者：Jonas Sauer
• 关键词：Muckenhoupt weights ; Stokes equation ; Spatially periodic ; Resolvent estimates ; 35B10 ; 35Q30 ; 76D05
• 刊名：Annali dell'Universita di Ferrara
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：61
• 期：2
• 页码：333-354
• 全文大小：528 KB
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• 作者单位：Jonas Sauer (1)
  
  1. Fachbereich Mathematik, Technische Universit?t, 64283, Darmstadt, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Geometry
  History of Mathematics
  Numerical Analysis
  Algebraic Geometry
  
• 出版者：Springer Milan
• ISSN：1827-1510

文摘

We consider spatially periodic Laplace and Stokes resolvent problems in the whole space and show corresponding weighted resolvent estimates with weights in the Muckenhoupt class. A main tool is the use of Fourier techniques on the Schwartz-Bruhat space and on the tempered distributions together with a weighted transference principle à la Andersen and Mohanty (Proc Amer Math Soc 137(5):1689-697, 2009) and a splitting of the function spaces into a mean-value free part and a nonperiodic part of functions defined on a lower-dimensional whole space, which then enables us to make use of a weighted Mikhlin multiplier theorem. Keywords Muckenhoupt weights Stokes equation Spatially periodic Resolvent estimates