On higher order extensions for the fractional Laplacian
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The technique of Caffarelli and Silvestre, characterizing the fractional Laplacian as the Dirichlet-to-Neumann map for a function U satisfying an elliptic equation in the upper half space with one extra spatial dimension, is shown to hold for general positive, non-integer orders of the fractional Laplace operator, by showing an equivalence between the H^s norm on the boundary and a suitable higher-order seminorm of U.
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Cited by 2 Pith papers
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Liouville theorems for the fractional Navier-Stokes equations with arbitrary asymptotic state at infinity
Proves complete Liouville theorems for 3D stationary fractional Navier-Stokes with arbitrary u_∞ at infinity for 1/2 ≤ s < 1 using refined L^p estimates and frequency localization.
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Liouville-type theorems for the stationary fractional Navier-Stokes equations in $\mathbb{R}^n$
Establishes Liouville-type theorems for stationary fractional Navier-Stokes in R^n under integrability and large-scale Morrey energy bounds, with corollary for finite fractional energy when n/3 ≤ α < (n+2)/3.
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