On the fractional Laplacian of variable order

2021/09/02 by Darve, Eric, D'Elia, Marta, Garrappa, Roberto +2
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2109.01060

Abstract

We present a novel definition of variable-order fractional Laplacian on Rn based on a natural generalization of the standard Riesz potential. Our definition holds for values of the fractional parameter spanning the entire open set (0, n/2). We then discuss some properties of the fractional Poisson's equation involving this operator and we compute the corresponding Green function, for which we provide some instructive examples for specific problems.

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