17 citations · 56 across the 22 of their papers we have counts for
5 papers · 1 filter
Non-Local Isoperimetric Problems
Agnese Di Castro, Berardo Ruffini, Novaga Matteo +1
We characterize the volume-constrained minimizers of a nonlocal free energy given by the difference of the -perimeter and the -perimeter, with smaller than . Exploitin…
A note on the hausdorff dimension of the singular set for minimizers of the mumford-shah energy
Camillo De Lellis, Matteo Focardi, Berardo Ruffini
We give a more elementary proof of a result by Ambrosio, Fusco and Hutchinson to estimate the Hausdorff dimension of the singular set of minimizers of the Mumford-Shah energy (see…
Stability theorems for GNS inequalities: a reduction principle to the radial case
Berardo Ruffini
A symmetrization techique, introduced by Cianchi, Fusco, Maggi and Pratelli concerning the Sobolev inequality, is adapted to the Gagliardo-Nirenberg-Sobolev inequality (GNS) to obt…
On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization
Michele Marini, Berardo Ruffini
We solve a class of weighted isoperimetric problems of the form where and are suitable f…
Brunn-Minkowski inequality for the 1-Riesz capacity and level set convexity for the 1/2-Laplacian
Matteo Novaga, Berardo Ruffini
We prove that that the 1-Riesz capacity satisfi es a Brunn-Minkowski inequality, and that the capacitary function of the 1/2-Laplacian is level set convex.