# Leibniz rules and Gauss–Green formulas in distributional fractional spaces

@article{Comi2021LeibnizRA,
title={Leibniz rules and Gauss–Green formulas in distributional fractional spaces},
author={Giovanni Eugenio Comi and Giorgio Stefani},
journal={Journal of Mathematical Analysis and Applications},
year={2021}
}
• Published 27 November 2021
• Mathematics
• Journal of Mathematical Analysis and Applications
5 Citations

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We study a general total variation denoising model with weighted L fidelity, where the regularizing term is a non-local variation induced by a suitable (non-integrable) kernel K, and the

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### Failure of the local chain rule for the fractional variation

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. We prove that the local version of the chain rule cannot hold for the fractional variation deﬁned in [7]. In the case n = 1, we prove a stronger result, exhibiting a function f ∈ BV α ( R ) such

### The fractional variation and the precise representative of $$BV^{\alpha ,p}$$ functions

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<jats:p>We continue the study of the fractional variation following the distributional approach developed in the previous works Bruè et al. (2021), Comi and Stefani (2019), Comi and Stefani (2019).

### A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I

• Art
Revista Matemática Complutense
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<jats:p>We continue the study of the space <jats:inline-formula><jats:alternatives><jats:tex-math>$$BV^\alpha ({\mathbb {R}}^n)$$</jats:tex-math><mml:math

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### The fractional variation and the precise representative of $$BV^{\alpha ,p}$$ functions

• Mathematics
Fractional Calculus and Applied Analysis
• 2022
<jats:p>We continue the study of the fractional variation following the distributional approach developed in the previous works Bruè et al. (2021), Comi and Stefani (2019), Comi and Stefani (2019).

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### A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I

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• 2022
<jats:p>We continue the study of the space <jats:inline-formula><jats:alternatives><jats:tex-math>$$BV^\alpha ({\mathbb {R}}^n)$$</jats:tex-math><mml:math

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