4 papers · 1 filter
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…
Linear quadratic optimal transport and interpolation inequalities
Luca Rizzi, Alec Jacopo Almo Schiavoni Piazza
This paper investigates the optimal transport problem within the framework of Linear Quadratic optimal control systems. We establish the well-posedness of the Monge problem and ana…
Interior singularity and branching of geodesics in real-analytic sub-Riemannian manifolds
Tommaso Rossi, Alec Jacopo Almo Schiavoni Piazza, Alessandro Socionovo
We study the regularity and branching of strictly abnormal minimizing geodesics in sub-Riemannian geometry. We construct examples of real-analytic sub-Riemannian manifolds admittin…