Approximation of solutions of fractional diffusions in compact metric measure spaces

AIMAR HUGO; ACTIS MARCELO

JOURNAL OF EVOLUTION EQUATIONS

BIRKHAUSER VERLAG AG

Lugar: BASEL; Año: 2017 vol. 17 p. 1259 - 1271

1424-3199

In this note we prove that the solutions to diusions associatedto fractional powers of the Laplacian in compact metric measure spaces canbe obtained as limits of the solutions to particular rescalings of some nonlocaldiusions with integrable kernels. The abstract approach considered here hasseveral particular and interesting instances. As an illustration of our resultswe present the case of dyadic metric measure spaces where the existence ofsolutions was already been proven in [1].