77 citations · 284 across the 43 of their papers we have counts for
36 papers · 1 filter
Unique Continuation Properties from one time for hyperbolic Schrödinger equations
Juan Antonio Barceló, Biagio Cassano, Luca Fanelli
In this paper, we investigate properties of unique continuation for hyperbolic Schrödinger equations with time-dependent complex-valued electric fields and time-independent real ma…
On uniqueness of solutions to the surface electromigration equation
Lucrezia Cossetti, Luca Fanelli, Felipe Linares
In this paper we investigate on uniqueness properties of solutions to the surface electromigration (SEM) equation, which is a generalisation of the more classical Zakharov-Kuznetso…
Uniform resolvent estimates for critical magnetic Schrödinger operators in 2D
Luca Fanelli, Junyong Zhang, Jiqiang Zheng
We study the -type uniform resolvent estimates for 2D-Schrödinger operators in scaling-critical magnetic fields, involving the Aharonov-Bohm model as a main example. As an…
Mass Propagation for Electromagnetic Schrödinger Evolutions
Juan Antonio Barceló, Biagio Cassano, Luca Fanelli
We investigate the validity of gaussian lower bounds for solutions to an electromagnetic Schrödinger equation with a bounded time-dependent complex electric potential and a time-in…
Kato-Ponce estimates for fractional sublaplacians
L. Fanelli, L. Roncal
We give a proof of commutator estimates for fractional powers of the sublaplacian on the Heisenberg group. Our approach is based on pointwise and estimates involving square f…
Improved Hardy-Rellich inequalities
Biagio Cassano, Lucrezia Cossetti, Luca Fanelli
We investigate Hardy-Rellich inequalities for perturbed Laplacians. In particular, we show that a non-trivial angular perturbation of the free operator typically improves the inequ…
Review on the stability of the Peregrine and related breathers
Miguel A. Alejo, Luca Fanelli, Claudio Muñoz
In this note, we review stability properties in energy spaces of three important nonlinear Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show th…
Dispersive estimates for 2D-wave equations with critical potentials
Luca Fanelli, Junyong Zhang, Jiqiang Zheng
We study the 2D-wave equation with a scaling-critical electromagnetic potential. This problem is doubly critical, because of the scaling invariance of the model and the singulariti…
Stability and instability of breathers in the Sasa-Satusuma and Nonlinear Schrödinger models
Miguel A. Alejo, Luca Fanelli, Claudio Muñoz
We consider the Sasa-Satsuma (SS) and Nonlinear Schrödinger (NLS) equations posed along the line, in 1+1 dimensions. Both equations are canonical integrable models, with sol…
The Akhmediev Breather is unstable
Miguel A. Alejo, Luca Fanelli, Claudio Muñoz
In this note, we give a rigorous proof that the NLS periodic Akhmediev breather is unstable. The proof follows the ideas in [17], in the sense that a suitable modification of the S…
Uniqueness results for Zakharov-Kuznetsov equation
Lucrezia Cossetti, Luca Fanelli, Felipe Linares
In this paper we study uniqueness properties of solutions to the Zakharov-Kuznetsov equation of plasma physic. Given two sufficiently regular solutions we prove that, i…
Dispersive estimates for the Dirac equation in an Aharonov-Bohm field
Federico Cacciafesta, Luca Fanelli
We prove local smoothing and weighted Strichartz estimates for the Dirac equation with a Aharonov-Bohm potential. The proof relies on an explicit representation of the solution bui…
Weak dispersive estimates for fractional Aharonov-Bohm-Schrödinger groups
F. Cacciafesta, L. Fanelli
We prove local smoothing, local energy decay and weighted Strichartz inequalities for fractional Schrödinger equations with a Aharonov-Bohm magnetic field in 2D. Explicit represent…
Gaussian decay of Harmonic Oscillators and related models
Biagio Cassano, Luca Fanelli
We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0-order complex perturbations, even if bounded, of th…
Frequency-dependent time decay of Schrödinger flows
L. Fanelli, V. Felli, M. Fontelos +1
We show that the presence of negative eigenvalues in the spectrum of the angular component of an electromagnetic Schrödinger hamiltonian generically produces a lack of the clas…
Improved time-decay for a class of scaling critical electromagnetic Schrödinger flows
Luca Fanelli, Gabriele Grillo, Hynek Kovarik
We consider a Schrödinger hamiltonian with scaling critical and time independent external electromagnetic potential, and assume that the angular operator associated to…
Time decay of scaling invariant Schroedinger equations on the plane
L. Fanelli, V. Felli, M. Fontelos +1
We prove the sharp L^1-L^{\infty} time-decay estimate for the 2D-Schroedinger equation with a general family of scaling critical electromagnetic potentials.
Sharp Hardy uncertainty principle and gaussian profiles of covariant Schrödinger evolutions
Biagio Cassano, Luca Fanelli
We prove a sharp version of the Hardy uncertainty principle for Schrödinger equations with external bounded electromagnetic potentials, based on logarithmic convexity properties of…
Hardy Uncertainty Principle and unique continuation properties of covariant Schrodinger flows
Juan Antonio Barcelo, Luca Fanelli, Susana Gutierrez +2
We prove a logarithmic convexity result for exponentially weighted -norms of solutions to electromagnetic Schrödinger equation, without needing to assume smallness of the magn…
Time decay of scaling critical electromagnetic Schrödinger flows
Luca Fanelli, Veronica Felli, Marco A. Fontelos +1
We obtain a representation formula for solutions to Schrödinger equations with a class of homogeneous, scaling-critical electromagnetic potentials. As a consequence, we prove the s…
The lack of compactness in the Sobolev-Strichartz inequalities
Luca Fanelli, Nicola Visciglia
We provide a general method to decompose any bounded sequence in into linear dispersive profiles generated by an abstract propagator, with a rest which is small in the a…
On the lack of dispersion for a class of magnetic Dirac flows
Naiara Arrizabalaga, Luca Fanelli, Andoni García
We show that global Strichartz estimates for magnetic Dirac operators generally fails, if the potentials do not decay fast enough at infinity. In order to prove this, we construct…
Carleman estimates and necessary conditions for the existence of waveguides
Luis Escauriaza, Luca Fanelli, Luis Vega
We study via Carleman estimates the sharpest possible exponential decay for {\it waveguide} solutions to the Laplace equation $$(\partial^2_t+\triangle)u=Vu+W\cdot(\partial_t,\nabl…
A priori estimates for the Helmholtz equation with electromagnetic potentials in exterior domains
Juan Antonio Barceló, Luca Fanelli, Alberto Ruiz +1
We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a domain, in dimension . We prove, by multiplier techniques in the sense of Mora…