We continue the study of the space BV α(Rn) of functions with bounded fractional variation in
Rn and of the distributional fractional Sobolev space Sα, p (Rn), with p∈[1,+∞] and α∈(0 …

We continue the study of the space BV α (R n) of functions with bounded fractional variation
in R n of order α∈(0, 1) introduced in our previous work (Comi and Stefani in J Funct Anal …

We study a class of non-local functionals that was introduced by Brezis et al.(2022), and can
be used to characterize functions of bounded variation. We give a new lower bound for the …

We consider a class of non-local functionals recently introduced by H. Brezis, A. Seeger, J.
Van Schaftingen, and P.-L. Yung, which offers a novel way to characterize functions with …

We consider a family of non-local and non-convex functionals, and we prove that their
Gamma-liminf is bounded from below by a positive multiple of the Sobolev norm or the total …

We consider the approximation of the total variation of a function by the family of nonlocal
and nonconvex functionals introduced by H. Brezis and H.-M. Nguyen in a recent paper. The …

On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the
total variation Page 1 CR Acad. Sci. Paris, Ser. I 356 (2018) 859–864 Contents lists available at …

We study the Γ-convergence of a family of non-local, non-convex functionals in L p (I) for p≥
1, where I is an open interval. We show that the limit is a multiple of the W 1, p (I) semi-norm …

Abstract We consider the Perona-Malik equation, which is a forward-backward parabolic
equation that can be seen as the formal gradient-flow of a non-convex functional, and we …

Let $ d\ge 1$, $ p\ge d $, and let $\Omega $ be a smooth bounded open subset of $\mathbb
{R}^ d $. We prove some exponential integrability in the spirit of Moser-Trudinger's …