6 papers
Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems
Roberto Ognibene, Bozhidar Velichkov
We consider energy-minimizing harmonic maps into trees and we prove the regularity of the singular part of the free interface near triple junction points. Precisely, by proving a n…
On the splitting of Neumann eigenvalues in perforated domains
Veronica Felli, Lorenzo Liverani, Roberto Ognibene
We address the problem of splitting of eigenvalues of the Neumann Laplacian under singular domain perturbations. We consider a domain perturbed by the excision of a small spherical…
A survey on the optimal partition problem
Roberto Ognibene, Bozhidar Velichkov
This survey synthesizes the current state of the art on the regularity theory for solutions to the optimal partition problem. Namely, we consider non-negative, vector-valued Sobole…
On asymptotics of Robin eigenvalues in the Dirichlet limit
Roberto Ognibene
We investigate the asymptotic behavior of the eigenvalues of the Laplacian with homogeneous Robin boundary conditions, when the (positive) Robin parameter is diverging. In this fra…
Asymptotics of nonlinear Robin energies
Giuseppe Buttazzo, Roberto Ognibene
This paper investigates the asymptotic behavior of a class of nonlinear variational problems with Robin-type boundary conditions on a bounded Lipschitz domain. The energy functiona…
Quantitative spectral stability for the Neumann Laplacian in domains with small holes
Veronica Felli, Lorenzo Liverani, Roberto Ognibene
The aim of the present paper is to investigate the behavior of the spectrum of the Neumann Laplacian in domains with little holes excised from the interior. More precisely, we cons…