10 citations · 15 across the 16 of their papers we have counts for
18 papers
On the stability of eigenvalues of varying bilinear forms in abstract Hilbertian settings and applications
Andrea Bisterzo, Roberto Ognibene, Prasun Roychowdhury +1
The aim of the present paper is to develop a spectral perturbation theory from a higher perspective. More precisely, we consider a one-parameter family of varying bilinear forms, e…
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…
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…
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 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…
Boundary regularity of the free interface in spectral optimal partition problems
Roberto Ognibene, Bozhidar Velichkov
We consider the problem of optimal partition of a domain with respect to the sum of the principal eigenvalues and we prove for the first time regularity results for the free interf…
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…
On the spectrum of sets made of cores and tubes
Francesca Bianchi, Lorenzo Brasco, Roberto Ognibene
We analyze the spectral properties of a particular class of unbounded open sets. These are made of a central bounded ``core'', with finitely many unbounded tubes attached to it. We…
Quantitative spectral stability for Aharonov-Bohm operators with many coalescing poles
Veronica Felli, Benedetta Noris, Roberto Ognibene +1
The behavior of simple eigenvalues of Aharonov-Bohm operators with many coalescing poles is discussed. In the case of half-integer circulation, a gauge transformation makes the pro…
Sharp behavior of Dirichlet--Laplacian eigenvalues for a class of singularly perturbed problems
Laura Abatangelo, Roberto Ognibene
We deepen the study of Dirichlet eigenvalues in bounded domains where a thin tube is attached to the boundary. As its section shrinks to a point, the problem is spectrally stable a…
Asymptotic behavior of constrained local minimizers in finite elasticity
Edoardo Mainini, Roberto Ognibene, Danilo Percivale
We provide an approximation result for the pure traction problem of linearized elasticity in terms of local minimizers of finite elasticity, under the constraint of vanishing avera…
A quantitative stability inequality for fractional capacities
Eleonora Cinti, Roberto Ognibene, Berardo Ruffini
The aim of this work is to show a non-sharp quantitative stability version of the fractional isocapacitary inequality. In particular, we provide a lower bound for the isocapacitary…
Eigenvalues of the Laplacian with moving mixed boundary conditions: the case of disappearing Neumann region
Veronica Felli, Benedetta Noris, Roberto Ognibene
We deal with eigenvalue problems for the Laplacian with varying mixed boundary conditions, consisting in homogeneous Neumann conditions on a vanishing portion of the boundary and D…
On a weighted two-phase boundary obstacle problem
Donatella Danielli, Roberto Ognibene
In this work we consider an inhomogeneous two-phase obstacle-type problem driven by the fractional Laplacian. In particular, making use of the Caffarelli-Silvestre extension, Almgr…
Eigenvalues of the Laplacian with moving mixed boundary conditions: the case of disappearing Dirichlet region
Veronica Felli, Benedetta Noris, Roberto Ognibene
In this work we consider the homogeneous Neumann eigenvalue problem for the Laplacian on a bounded Lipschitz domain and a singular perturbation of it, which consists in prescribing…
On fractional multi-singular Schrödinger operators: positivity and localization of binding
Veronica Felli, Debangana Mukherjee, Roberto Ognibene
In this work we investigate positivity properties of nonlocal Schrödinger type operators, driven by the fractional Laplacian, with multipolar, critical, and locally homogeneous pot…
Sharp Convergence Rate of Eigenvalues in a Domain with a Shrinking Tube
Veronica Felli, Roberto Ognibene
In this paper we consider a class of singularly perturbed domains, obtained by attaching a cylindrical tube to a fixed bounded region and letting its section shrink to zero. We use…