5 papers
Scattering Theory For 3D Cubic Damped Magnetic Schrödinger Equation
Luca Fanelli, Haruya Mizutani, Yilin Song +2
We consider the three-dimensional defocusing cubic nonlinear Schrödinger equation with variable coefficients, a magnetic potential, and a non-negative localized damping term, \[ i\…
Magnetic uncertainty in variable geometry
Luca Fanelli, Yilin Song, Ying Wang +2
In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence o…
Unweighted Hardy Inequalities on the Heisenberg Group and in Step-Two Carnot Groups
Lorenzo d'Arca, Luca Fanelli, Valentina Franceschi +1
We establish unweighted Hardy-type inequalities on step-two Carnot groups with one-dimensional vertical layer, with explicit lower bounds for the optimal Hardy constant. The approa…
A relativistic Hardy-type inequality with minimisers
Luca Fanelli, Fabio Pizzichillo
In this paper, we prove a sharp, weighted Hardy-type inequality for the Dirac operator. A key feature of our result is that the inequality is not only sharp but also attained, and…
Quantitative Hardy inequality for magnetic Hamiltonians
Luca Fanelli, Hynek Kovarik
In this paper we present a new method of proof of Hardy type inequalities for two-dimensional quantum Hamiltonians with a magnetic field of finite flux. Our approach gives a quanti…