Approximation of solutions of fractional dif- fusions in compact metric measure spaces

ACTIS, MARCELO; AIMAR, HUGO

JOURNAL OF EVOLUTION EQUATIONS

BIRKHAUSER VERLAG AG

Lugar: BASEL; Año: 2017 p. 1 - 13

1424-3199

In this note we prove that the solutions to diffusions associated to fractional powers of the Laplacian in compact metric measure spaces can be obtained as limits of the solutions to particular rescalings of some nonlocaldiffusions with integrable kernels. The abstract approach considered here hasseveral particular and interesting instances. As an illustration of our results we present the case of dyadic metric measure spaces where the existence of solutions was already been proven in [1]. References: 1. Marcelo Actis and Hugo Aimar, Dyadic nonlocal diffusions in metric measure spaces, Fract. Calc. Appl. Anal. 18 (2015), no. 3, 762?788. MR 3351499