# 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} }

## 5 Citations

### Non-local $BV$ functions and a denoising model with $L^1$ fidelity

- Mathematics
- 2022

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…

### Extending linear growth functionals to functions of bounded fractional variation

- Mathematics
- 2022

. In this paper we consider the minimization of a novel class of fractional linear growth functionals involving the Riesz fractional gradient. These functionals lack the coercivity properties in the…

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

- Mathematics
- 2022

. 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

- MathematicsFractional 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).…

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

- ArtRevista Matemática Complutense
- 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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### Correction to: On Nonlocal Variational and Quasi-Variational Inequalities with Fractional Gradient

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- 2021

A Correction to this paper has been published: https://doi.org/10.1007/s00245-019-09610-0

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

- MathematicsFractional 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).…

### On a Class of Fractional Obstacle Type Problems Related to the Distributional Riesz Derivative

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In this paper we study localization properties of the Riesz $s$-fractional gradient $D^s u$ of a vectorial function $u$ as $s \nearrow 1$. The natural space to work with $s$-fractional gradients is…

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The Paley–Littlewood square function

### 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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Abstract In this paper we continue to advance the theory regarding the Riesz fractional gradient in the calculus of variations and fractional partial differential equations begun in an earlier work…