7 citations · 15 across the 14 of their papers we have counts for
17 papers
Lower bounds and Poincaré inequality for the Brezis-Seeger-Van Schaftingen-Yung functionals
Nicola Picenni
We consider a family of non-local and non-convex functionals depending on three real parameters , which was introduced by H. Brezis, A. Seeger, J. Van Schaftingen and P. L…
Another look at a notion of fractional mass in codimension two
Michele Caselli, Mattia Freguglia, Nicola Picenni
We study a notion of fractional -mass for codimension-two currents on closed Riemannian manifolds, defined via energy minimization with a prescribed Jacobian constraint. We prov…
Saddle solution to the complex Ginzburg-Landau system in three dimensions
Michele Caselli, Nicola Picenni
We construct an entire saddle solution to the non-magnetic complex Ginzburg-Landau system in three dimensions, whose zero set is the union of two perpendicular, intersecting lines,…
Symmetry breaking for local minimizers of a free discontinuity problem
Massimo Gobbino, Nicola Picenni
We study a functional defined on the class of piecewise constant functions, combining a jump penalization, which discourages discontinuities, with a fidelity term that penalizes de…
Coercivity and Gamma-convergence of the -energy of sphere-valued Sobolev maps
Michele Caselli, Mattia Freguglia, Nicola Picenni
We consider sequences of maps from an -dimensional domain into the -sphere, which satisfy a natural -energy growth, as approaches from below. We prove that…
A nonlocal approximation of the area in codimension two
Michele Caselli, Mattia Freguglia, Nicola Picenni
For we introduce a notion of fractional -mass on -dimensional closed, orientable surfaces in . Moreover, we prove its -convergence, with respect to…
Multi-scale analysis of minimizers for a second order regularization of the Perona-Malik functional
Massimo Gobbino, Nicola Picenni
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 thes…
Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms
Massimo Gobbino, Nicola Picenni
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 var…
New estimates for a class of non-local approximations of the total variation
Nicola Picenni
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 wit…
Staircasing effect for minimizers of the one-dimensional discrete Perona-Malik functional
Nicola Picenni
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 conte…
Monotonicity properties of limits of solutions to the semi-discrete scheme for the Perona-Malik equation
Massimo Gobbino, Nicola Picenni
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…
On a conjecture of De Giorgi about the phase-field approximation of the Willmore functional
Giovanni Bellettini, Mattia Freguglia, Nicola Picenni
In 1991 De Giorgi conjectured that, given , if stands for the density of the Allen-Cahn energy and represents its first variation, then $\int […
A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona-Malik functional
Massimo Gobbino, Nicola Picenni
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 th…
On the characterization of constant functions through nonlocal functionals
Massimo Gobbino, Nicola Picenni
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 f…
On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation
Clara Antonucci, Massimo Gobbino, Matteo Migliorini +1
We consider the family of non-local and non-convex functionals introduced by H. Brezis and H.-M. Nguyen in a recent paper. These functionals Gamma-converge to a multiple of the Sob…
On the gap between Gamma-limit and pointwise limit for a non-local approximation of the total variation
Clara Antonucci, Massimo Gobbino, Nicola Picenni
We consider the approximation of the total variation of a function by the family of non-local and non-convex functionals introduced by H. Brezis and H.-M. Nguyen in a recent paper.…
Optimal constants for a non-local approximation of Sobolev norms and total variation
Clara Antonucci, Massimo Gobbino, Matteo Migliorini +1
We consider the family of non-local and non-convex functionals proposed and investigated by J. Bourgain, H. Brezis and H.-M. Nguyen in a series of papers of the last decade. It was…