Calculus of Variations and Geometric Measure Theory

A. Leaci - F. Tomarelli

Riemann–Liouville Fractional Sobolev and Bounded Variation Spaces

created by leaci on 19 Jan 2022


Published Paper

Inserted: 19 jan 2022

Journal: Axioms
Volume: 11
Number: 1
Pages: 30-60
Year: 2022
Links: Published paper


We establish some properties of the bilateral Riemann–Liouville fractional derivative $D^s$. We set the notation, and study the associated Sobolev spaces of fractional order $s$, denoted by $W^{s,1}(a,b)$, and the fractional bounded variation spaces of fractional order $s$, denoted by $BV^s(a,b)$. Examples, embeddings and compactness properties related to these spaces are addressed, aiming to set a functional framework suitable for fractional variational models for image analysis.

Keywords: calculus of variations, Sobolev spaces, bounded variation functions, fractional derivatives, Abel equation