25 citations · 127 across the 25 of their papers we have counts for
9 papers · 1 filter
The nonlocal isoperimetric problem for polygons: Hardy-Littlewood and Riesz inequalities
Beniamin Bogosel, Dorin Bucur, Ilaria Fragalà
Given a non-increasing and radially symmetric kernel in , we investigate counterparts of the classical Hardy-Littlewood and Riesz inequa…
On the honeycomb conjecture for Robin Laplacian eigenvalues
Dorin Bucur, Ilaria Fragala
We prove that the optimal cluster problem for the sum of the first Robin eigenvalue of the Laplacian, in the limit of a large number of convex cells, is asymptotically solved by (t…
Phase field approach to optimal packing problems and related Cheeger clusters
Beniamin Bogosel, Dorin Bucur, Ilaria Fragala
In a fixed domain of we study the asymptotic behaviour of optimal clusters associated to -Cheeger constants and natural energies like the sum or maximum: we prove th…
On the honeycomb conjecture for a class of minimal convex partitions
Dorin Bucur, Ilaria Fragalà, Bozhidar Velichkov +1
We prove that the planar hexagonal honeycomb is asymptotically optimal for a large class of optimal partition problems, in which the cells are assumed to be convex, and the criteri…
A duality theory for non-convex problems in the Calculus of Variations
Guy Bouchitté, Ilaria Fragalà
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear progr…
A variational method for second order shape derivatives
Guy Bouchitté, Ilaria Fragalà, Ilaria Lucardesi
We consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet-Neumann boundary conditions. We…