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Extension Problems Related to the Higher Order Fractional Laplacian
CHEN, Yu Kang - Personal Name
LEI, Zhen - Personal Name
WEI, Chang Hua - Personal Name
Caffarelli and Silvestre [Comm. Part. Diff. Eqs., 32, 1245–1260 (2007)] characterized the fractional Laplacian (−Δ) 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 L p norm using the Caffarelli–Silvestre’s extension technique.Keywords Fractional Laplacian, quasi-geostrophic equations, energy equality
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| EB00000003407K | Available |
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Yu Kang CHEN , Zhen LEI , Chang Hua WEI
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