4 papers · 1 filter
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…