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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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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description 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.
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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
title Extension Problems Related to the Higher Order Fractional Laplacian
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