arXiv subjects

Alberto Fiorini

Publications and source records attributed to Alberto Fiorini.

2 recordsLinked to original sources

arXiv2026

The periodic Wulff problem in two dimensions

We characterize the minimizers of the anisotropic perimeter in the flat torus under an area constraint. We show that, depending on the area, the periodic global minimizer undergoes two phase transitions, changing from a droplet (a rescaled Wulff shape) to a flat band wrapping around the torus in a preferred direction determined by the anisotropy (lamellar phase), and finally to a bubble (the complement of a rescaled Wulff shape). For certain non-symmetric surface tensions, the lamellar phase is absent altogether; for other non regular surface tensions, there exist infinitely many minimizing configurations coexisting with the lamellar phase.

math.AP↗

arXiv2026

Local and global minimality of the lamella for the anisotropic Ohta-Kawasaki energy

In this paper we consider the volume-constrained minimization of a variant of the Ohta-Kawasaki functional with an anisotropic surface energy replacing the standard perimeter. Following and suitably adapting the second variation approach devised in arXiv:1211.0164, we prove local minimality results for the horizontal lamellar configuration, in analogy with the isotropic case, under the assumption that the anisotropy is uniformly elliptic. If instead the Wulff shape of the anisotropy has upper and lower horizontal facets, we prove that the lamella exhibits a rigid behavior and is an isolated local minimizer for all parameter values. We conclude by showing some global minimality results, mostly focusing on the planar case.

math.AP↗