On the fractional Laplacian of variable order [article]

Eric Darve, Marta D'Elia, Roberto Garrappa, Andrea Giusti, Natalia L. Rubio
2021 arXiv   pre-print
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.
arXiv:2109.01060v1 fatcat:yclb2z5zsrh7foonfbptxdenqi