Zobrazeno 1 - 10
of 38
pro vyhledávání: '"PICENNI, NICOLA"'
For $s\in (0,1)$ we introduce a notion of fractional $s$-mass on $(n-2)$-dimensional closed, orientable surfaces in $\R^n$. Moreover, we prove its $\Gamma$-convergence, with respect to the flat topology, and pointwise convergence to the $(n-2)$-dimen
Externí odkaz:
http://arxiv.org/abs/2406.13696
Autor:
Gobbino, Massimo, Picenni, Nicola
We investigate the asymptotic behavior of minimizers for the singularly perturbed Perona-Malik functional in one dimension. In a previous study, we have shown that blow-ups of these minimizers at a suitable scale converge to staircase-like piecewise
Externí odkaz:
http://arxiv.org/abs/2311.14565
Autor:
Gobbino, Massimo, Picenni, Nicola
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 variation. As a by-product, we answer some open questions concerning the
Externí odkaz:
http://arxiv.org/abs/2311.05560
Autor:
Picenni, Nicola
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 bounded variation. We give a positive answer to an open question rel
Externí odkaz:
http://arxiv.org/abs/2307.16471
Autor:
Picenni, Nicola
We consider the one-dimensional Perona-Malik functional, that is the energy associated to the celebrated forward-backward equation introduced by P. Perona and J. Malik in the context of image processing, with the addition of a forcing term. We discre
Externí odkaz:
http://arxiv.org/abs/2306.08652
Autor:
Gobbino, Massimo, Picenni, Nicola
We consider generalized solutions of the Perona-Malik equation in dimension one, defined as all possible limits of solutions to the semi-discrete approximation in which derivatives with respect to the space variable are replaced by difference quotien
Externí odkaz:
http://arxiv.org/abs/2304.04729
In 1991 De Giorgi conjectured that, given $\lambda >0$, if $\mu_\varepsilon$ stands for the density of the Allen-Cahn energy and $v_\varepsilon$ represents its first variation, then $\int [v_\varepsilon^2 + \lambda] d\mu_\varepsilon$ should $\Gamma$-
Externí odkaz:
http://arxiv.org/abs/2206.04649
Autor:
Gobbino, Massimo, Picenni, Nicola
We consider the Perona-Malik functional in dimension one, namely an integral functional whose Lagrangian is convex-concave with respect to the derivative, with a convexification that is identically zero. We approximate and regularize the functional b
Externí odkaz:
http://arxiv.org/abs/2205.02467
Autor:
Picenni, Nicola
Publikováno v:
In Journal of Functional Analysis 1 July 2024 287(1)
Autor:
Gobbino, Massimo, Picenni, Nicola
We address a classical open question by H.Brezis and R.Ignat concerning the characterization of constant functions through double integrals that involve difference quotients. Our first result is a counterexample to the question in its full generality
Externí odkaz:
http://arxiv.org/abs/2004.00608