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arXiv · 1302.4413

On higher order extensions for the fractional Laplacian

Ray Yang
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Abstract

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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Ray Yang. 2013-02-18. On higher order extensions for the fractional Laplacian. https://arxiv.org/abs/1302.4413

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