Now showing items 21-40 of 44

• #### On the improvement of the Hardy inequality due to singular magnetic fields ﻿

(2018-07-12)
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ...
• #### On the improvement of the Hardy inequality due to singular magnetic fields ﻿

(2018-07-12)
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ...
• #### On the improvement of the Hardy inequality due to singular magnetic fields ﻿

(2020-09-01)
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ...
• #### On the regularity of solutions to the k-generalized korteweg-de vries equation ﻿

(2018-07)
This work is concerned with special regularity properties of solutions to the k-generalized Korteweg-de Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ...
• #### On the regularity of solutions to the k-generalized korteweg-de vries equation ﻿

(2018-01-01)
This work is concerned with special regularity properties of solutions to the k-generalized Korteweg-de Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ...
• #### On the Relationship between the One-Corner Problem and the $M-$Corner Problem for the Vortex Filament Equation ﻿

(2018-06-28)
In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular M-corner polygon as initial datum can be explained at infinitesimal times as the superposition of M one-corner initial ...
• #### On the unique continuation of solutions to non-local non-linear dispersive equations ﻿

(2020-08-02)
We prove unique continuation properties of solutions to a large class of nonlinear, non-local dispersive equations. The goal is to show that if (Formula presented.) are two suitable solutions of the equation defined in ...
• #### Relativistic Hardy Inequalities in Magnetic Fields ﻿

(2014-12-31)
We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality ...
• #### Riemann's non-differentiable function and the binormal curvature flow ﻿

(2020-07-14)
We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object ...
• #### 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 ...
• #### Shell interactions for Dirac operators: On the point spectrum and the confinement ﻿

(2015-12-31)
Spectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$ and $V$ is a measure-valued potential. The ...
• #### Singularity formation for the 1-D cubic NLS and the Schrödinger map on $\mathbb{S}^2$ ﻿

(2017-02-02)
In this note we consider the 1-D cubic Schrödinger equation with data given as small perturbations of a Dirac-$\delta$ function and some other related equations. We first recall that although the problem for this type of ...
• #### 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, ...
• #### Spectral stability of Schrödinger operators with subordinated complex potentials ﻿

(2018-06-28)
We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness condition. By developing ...
• #### Static and Dynamical, Fractional Uncertainty Principles ﻿

(2021-03)
We study the process of dispersion of low-regularity solutions to the Schrödinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get ...
• #### A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions ﻿

(2016-12-21)
We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a $C^2$-compact surface without boundary. To do so we are lead to study the layer potential induced by the ...
• #### The dynamics of vortex filaments with corners ﻿

(2015-07-01)
This paper focuses on surveying some recent results obtained by the author together with V. Banica on the evolution of a vortex filament with one corner according to the so-called binormal flow. The case of a regular polygon ...
• #### The initial value problem for the binormal flow with rough data ﻿

(2015-12-31)
In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove that under suitable conditions on the ...
• #### The Vortex Filament Equation as a Pseudorandom Generator ﻿

(2015-08-01)
In this paper, we consider the evolution of the so-called vortex filament equation (VFE), $$X_t = X_s \wedge X_{ss},$$ taking a planar regular polygon of M sides as initial datum. We study VFE from a completely novel ...
• #### Uniqueness properties for discrete equations and Carleman estimates ﻿

(2017-03-25)
Using Carleman estimates, we give a lower bound for solutions to the discrete Schrödinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of ...