Extension Problems Related to the Higher Order Fractional Laplacian

作     者：Yu Kang CHEN Zhen LEI Chang Hua WEI 

作者机构：School of Mathematical Sciences Fudan University Shanghai 200433 P. R. China School of Mathematical Sciences and Shanghai Center for Mathematical Sciences Fudan University Shanghai 200433 P. R. China Department of Mathematics Zhejiang Sci-Tech University Hangzhou 310018 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2018年第34卷第4期

页      面：655-661页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：part supported by NSFC(Grant Nos.11725102,11421061 and 11701517) Shanghai Talent Development Fund and SGST(Grant No.09DZ2272900) 

主　　题：Fractional Laplacian quasi-geostrophic equations energy equality 

摘      要：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.