Calculus of Variations and Geometric Measure Theory

A. Carbotti - S. Dipierro - E. Valdinoci

Local density of solutions of time and space fractional equations

created by carbotti on 21 Mar 2020
modified on 23 Mar 2020



Inserted: 21 mar 2020
Last Updated: 23 mar 2020

Year: 2018

ArXiv: 1810.08448 PDF


We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account anomalous diffusion, with possible fractional components in both space and time. The operators studied comprise the case of the sum of classical and fractional Laplacians, possibly of different orders, in the space variables, and classical or fractional derivatives in the time variables. This type of approximation results shows that space-fractional and time-fractional equations exhibit a variety of solutions which is much richer and more abundant than in the case of classical diffusion. This preprint is part of the Monograph "Local density of solutions to fractional equations", edited by the same authors and published in August, 2019.