Luis Caffarelli, Luis Silvestre
Published 2006-08-25, updated 2007-02-13Version 2
The operator square root of the Laplacian $(-\lap)^{1/2}$ can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this paper we obtain similar characterizations for general fractional powers of the Laplacian and other integro-differential operators. From those characterizations we derive some properties of these integro-differential equations from purely local arguments in the extension problems.
Uniqueness and Nondegeneracy of Ground States for $(-Δ)^s Q + Q - Q^{α+1} = 0$ in $\mathbb{R}$
Variational inequalities for the fractional Laplacian
On the Asymptotic Analysis of Problems Involving Fractional Laplacian in Cylindrical Domains Tending to Infinity
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