7 papers
A Homogenized Maz'ya--Shaposhnikova formula
Andrea Braides, Marco Picerni, Alec Jacopo Almo Schiavoni Piazza
We study the asymptotic behaviour of fractional Gagliardo-type energies with a periodic, bounded and bounded away from zero coefficient depending on both variables, in the joint li…
Homogenization and averaging in the Bourgain-Brezis-Mironescu limit
Andrea Braides, Stefano Mannella, Alec Jacopo Almo Schiavoni Piazza
We study the simultaneous asymptotic behaviour of homogenization and the Bourgain--Brezis--Mironescu limit for quadratic fractional energies with periodic coefficients. The functio…
Homogenization in fractional phase transitions at the critical scale
Andrea Braides, Abdilaziz Zoir Ugli Komilov
We analyze fractional phase-transition energies with periodic hetero\-genei\-ties at the critical scaling. We prove that the -limit is a sharp-interface functional who…
Dimension reduction of fractional Sobolev seminorms on thin domains
Andrea Braides, Andrea Pinamonti, Margherita Solci
We study the asymptotic behaviour of Gagliardo seminorms in defined on thin films $Ω_\e=ω\times(0,\e)$. The first relevant order is $\e^{1-2s}$, at which the corresponding li…
Asymptotic analysis of higher-order perturbations of the Perona--Malik functional
Andrea Braides, Irene Fonseca
The Gamma-limit of higher-order singular perturbations of the Perona-Malik functional is analyzed. The energies considered combine the critically scaled logarithmic term with a k-t…
Modulated phases in Ising systems with long-range antiferromagnetic and short-range ferromagnetic interactions
Andrea Braides, Fabrizio Caragiulo
We consider large spin systems with short-range ferromagnetic interactions and long-range antiferromagnetic interactions subjected to periodic boundary conditions which have been p…
Microstructures and anti-phase boundaries in long-range lattice systems
Andrea Braides, Edoardo Voglino, Matteo Zanardini
We study the effect of long-range interactions in non-convex one-dimensional lattice systems in the simplified yet meaningful assumption that the relevant long-range interactions a…