Fractional sobolev spaces and functions of bounded variation of one variable-Reference-Cited by-同舟云学术

Fractional sobolev spaces and functions of bounded variation of one variable

Published:2017-08-01 Issue:4 Volume:20 Page:936-962
ISSN:1311-0454
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Bergounioux Maïtine¹,Leaci Antonio²,Nardi Giacomo³,Tomarelli Franco⁴

Affiliation:

1. Laboratoire MAPMO, CNRS, UMR 7349 Fédération Denis Poisson, FR 2964 Université d’Orléans , B.P. 6759 45067 Orléans cedex 2, France

2. Università del Salento Dipartimento di Matematica e Fisica “Ennio De Giorgi” I 73100 Lecce , Italy

3. Institut Pasteur, Laboratoire d’Analyse d’Images Biologiques CNRS , UMR 3691 Paris , France

4. Politecnico di Milano , Dipartimento di Matematica Piazza “Leonardo da Vinci” , 32 I 20133 Milano , Italy

Abstract

Abstract We investigate the 1D Riemann-Liouville fractional derivative focusing on the connections with fractional Sobolev spaces, the space BV of functions of bounded variation, whose derivatives are not functions but measures and the space SBV, say the space of bounded variation functions whose derivative has no Cantor part. We prove that SBV is included in W s,1 for every s ∈ (0, 1) while the result remains open for BV. We study examples and address open questions.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2017-0049/pdf

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