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Bilinear identities involving the k-plane transform and Fourier extension operators
(2019-11-30)
We prove certain L2pRnq bilinear estimates for Fourier extension operators associ- ated to spheres and hyperboloids under the action of the k-plane transform. As the estimates are L2-based, they follow from bilinear ...
Some geometric properties of Riemann’s non-differentiable function
(2019-11-06)
Riemann’s non-differentiable function is a celebrated example of a continuous but almost nowhere differentiable function. There is strong numeric evidence that one of its complex versions represents a geometric trajectory ...
Carleman type inequalities for fractional relativistic operators
(2019-09-22)
In this paper, we derive Carleman estimates for the fractional relativistic operator. Firstly, we consider changing-sign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity ...
On the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsion
(2019-09-03)
In this paper, we consider the evolution of the Vortex Filament equa- tion (VFE):
Xt = Xs ∧ Xss,
taking M-sided regular polygons with nonzero torsion as initial data. Us- ing algebraic techniques, backed by numerical ...
Asymptotic behaviour of some nonlocal equations in mathematical biology and kinetic theory
(2019-09)
We study the long-time behaviour of solutions to some partial differential equations arising in modeling of several biological and physical phenomena. In this work, the type of the equations we consider is mainly nonlocal, ...
Some lower bounds for solutions of Schrodinger evolutions
(2019-08-21)
We present some lower bounds for regular solutions of Schr odinger equations with bounded and time dependent complex potentials. Assuming that the solution has some positive mass at time zero within a ball of certain radius, ...
On the energy of critical solutions of the binormal flow
(2019-07-20)
The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisen- berg model in ferromagnetism, and the 1-D cubic Schr ...
A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
(2019-07-02)
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 potentials V of Coulomb type: we characterise ...
A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator
(2019-06)
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 potentials $\mathbf V$ of Coulomb type: ...
Self-similar dynamics for the modified Korteweg-de Vries equation
(2019-04-09)
We prove a local well posedness result for the modified Korteweg-de Vries equa- tion in a critical space designed so that is contains self-similar solutions. As a consequence, we can study the flow of this equation around ...