5 papers · 1 filter
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…
A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
Biagio Cassano, Fabio Pizzichillo, Luis Vega
We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued…
Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations
Biagio Cassano, Fabio Pizzichillo
We determine explicitly a boundary triple for the Dirac operator in , for and $\mathbb V(x)= |x|^{-1} ( ν\mathb…
Sharp exponential localization for solutions of the Perturbed Dirac Equation
Biagio Cassano
We determine the largest non-trivial rate of exponential decay at infinity for solutions to the Dirac equation \begin{equation*} \mathcal{D}_n ψ+ \mathbb{V} ψ= 0 \quad \text{ in }\…
Scattering in the energy space for the NLS with variable coefficients
Biagio Cassano, Piero D'Ancona
We consider the NLS with variable coefficients in dimension \begin{equation*} i \partial_t u - Lu +f(u)=0, \qquad Lv=\nabla^{b}\cdot(a(x)\nabla^{b}v)-c(x)v, \qquad \nabla^{…