Extension Problems Related to the Higher Order Fractional Laplacian

Abstract Caffarelli and Silvestre [Comm. Part. Diff. Eqs., 32, 1245-1260 （2007）] characterized the fractional Laplacian （-△）s as an operator maps Dirichlet boundary condition to Neumann condition via the harmonic extension problem to the upper half space for 0 〈 s 〈 1. In this paper, we extend this...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2018-04, Vol.34 (4), p.655-661
Main Authors: Chen, Yu Kang, Lei, Zhen, Wei, Chang Hua
Format: Article
Language:English
Subjects:
Boundary conditions
Dirichlet problem
Laplace transforms
Mathematical analysis
Mathematics
Mathematics and Statistics
拉普拉斯算符
延期
Dirichlet
Neumann
扩展问题
地球自转
操作符
空格
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Summary:Abstract Caffarelli and Silvestre [Comm. Part. Diff. Eqs., 32, 1245-1260 （2007）] characterized the fractional Laplacian （-△）s as an operator maps Dirichlet boundary condition to Neumann condition via the harmonic extension problem to the upper half space for 0 〈 s 〈 1. In this paper, we extend this result to all s 〉 0. We also give a new proof to the dissipative a priori estimate of quasi-geostrophic equations in the framework of Lp norm using the Caffarelli-Silvestre＇s extension technique.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-017-7325-6