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arXiv · 1603.05033

Fractional Sobolev Spaces and Functions of Bounded Variation

M. Bergounioux·A. Leaci·G. Nardi·F. Tomarelli
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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 $s \in (0,1)$ while the result remains open for $BV$. We study examples and address open questions.

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M. Bergounioux, A. Leaci, G. Nardi, F. Tomarelli. 2016-03-16. Fractional Sobolev Spaces and Functions of Bounded Variation. https://arxiv.org/abs/1603.05033

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