Calculus of Variations and Geometric Measure Theory

A distributional approach to fractional spaces and fractional variation

Giorgio Stefani (Scuola Internazionale Superiore di Studi Avanzati (SISSA))

created by miranda on 01 Mar 2021

4 mar 2021 -- 15:00   [open in google calendar]

Dipartimento di Matematica e Informatica di Ferrara (on-line)


We study the fractional SobolevBessel spaces and a new notion of fractional variation from a new distributional point of view, exploiting suitable notions of fractional gradient and fractional divergence already existing in the literature. Our approach provides several natural parallelisms between the fractional framework and the classical theory of SobolevDe Giorgi. After a brief summary on the basic features of the fractional operators involved, we will present a panoramic view of the theory we were able to develop so far. This is an ongoing project with G. E. Comi, and some of the results were obtained in collaboration also with E. Bruè, M. Calzi and D. Spector.