77 citations · 285 across the 27 of their papers we have counts for
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Failure of the Pólya-Szegő inequality for the fractional gradient
Giorgio Stefani
We prove that the Pólya-Szegő inequality for the norm of the Riesz fractional -gradient fails for every and , thus providing a negative answer to a…
On sets with finite distributional fractional perimeter
Giovanni E. Comi, Giorgio Stefani
We continue the study of the fine properties of sets having locally finite distributional fractional perimeter. We refine the characterization of their blow-ups and prove a Leibniz…
Fractional divergence-measure fields, Leibniz rule and Gauss-Green formula
Giovanni E. Comi, Giorgio Stefani
Given and , we define the space of vector fields whose -divergence is a finite Radon measure, extending the…
Non-local functions and a denoising model with fidelity
Konstantinos Bessas, Giorgio Stefani
We study a general total variation denoising model with weighted fidelity, where the regularizing term is a non-local variation induced by a suitable (non-integrable) kernel…
Failure of the local chain rule for the fractional variation
Giovanni E. Comi, Giorgio Stefani
We prove that the local version of the chain rule cannot hold for the fractional variation defined in arXiv:1809.08575. In the case , we prove a stronger result, exhibiting…
Leibniz rules and Gauss-Green formulas in distributional fractional spaces
Giovanni E. Comi, Giorgio Stefani
We apply the results established in arXiv:2109.15263 to prove some new fractional Leibniz rules involving and functions, following the distributional approach…
The fractional variation and the precise representative of functions
Giovanni E. Comi, Daniel Spector, Giorgio Stefani
We continue the study of the fractional variation following the distributional approach developed in the previous works arXiv:1809.08575, arXiv:1910.13419 and arXiv:2011.03928. We…
A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics II
Elia Bruè, Mattia Calzi, Giovanni E. Comi +1
We continue the study of the space of functions with bounded fractional variation in and of the distributional fractional Sobolev space $S^{α,p}(\…
A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I
Giovanni E. Comi, G. Stefani
We continue the study of the space of functions with bounded fractional variation in of order introduced in arXiv:1809.08575, by dea…
A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up
Giovanni E. Comi, Giorgio Stefani
We introduce the new space of functions with bounded fractional variation in of order via a new distributional approach exploiting…