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arXiv · 2109.01060

On the fractional Laplacian of variable order

Eric Darve·Marta D'Elia·Roberto Garrappa·Andrea Giusti·Natalia L. Rubio
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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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Eric Darve, Marta D'Elia, Roberto Garrappa, Andrea Giusti, Natalia L. Rubio. 2021-09-02. On the fractional Laplacian of variable order. https://arxiv.org/abs/2109.01060

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