Browsing Linear and NonLinear Waves by Author "Vega, L."
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On the improvement of the Hardy inequality due to singular magnetic fields
Fanelli, L.; Krejcirik, D.; Laptev, A.; Vega, L. (20180712)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the AharonovBohm field in all dimensions and establish a sharp Hardytype ... 
On the improvement of the Hardy inequality due to singular magnetic fields
Fanelli, L.; Krejcirik, D.; Laptev, A.; Vega, L. (20180712)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the AharonovBohm field in all dimensions and establish a sharp Hardytype ... 
On the improvement of the Hardy inequality due to singular magnetic fields
Fanelli, L.; Krejčiřík, D.; Laptev, A.; Vega, L. (20200901)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the AharonovBohm field in all dimensions and establish a sharp Hardytype ... 
On the regularity of solutions to the kgeneralized kortewegde vries equation
Kenig, C.E.; Linares, F.; Ponce, G.; Vega, L. (201807)This work is concerned with special regularity properties of solutions to the kgeneralized Kortewegde 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 kgeneralized kortewegde vries equation
Kenig, C. E.; Linares, F.; Ponce, G.; Vega, L. (20180101)This work is concerned with special regularity properties of solutions to the kgeneralized Kortewegde Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ... 
On the Relationship between the OneCorner Problem and the $M$Corner Problem for the Vortex Filament Equation
De la Hoz, F.; Vega, L. (20180628)In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular Mcorner polygon as initial datum can be explained at infinitesimal times as the superposition of M onecorner initial ... 
On the unique continuation of solutions to nonlocal nonlinear dispersive equations
Kenig, C. E.; Pilod, D.; Ponce, G.; Vega, L. (20200802)We prove unique continuation properties of solutions to a large class of nonlinear, nonlocal 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
Fanelli, L.; Vega, L.; Visciglia, N. (20141231)We deal with Dirac operators with external homogeneous magnetic fields. Hardytype inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality ... 
Riemann's nondifferentiable function and the binormal curvature flow
Banica, V.; Vega, L. (20200714)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 ... 
Selfsimilar dynamics for the modified Kortewegde Vries equation
Correia, S.; Côte, R.; Vega, L. (20190409)We prove a local well posedness result for the modified Kortewegde Vries equa tion in a critical space designed so that is contains selfsimilar 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
Arrizabalaga, N.; Mas, A.; Vega, L. (20151231)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 measurevalued potential. The ... 
Singularity formation for the 1D cubic NLS and the Schrödinger map on $\mathbb{S}^2$
Banica, V.; Vega, L. (20170202)In this note we consider the 1D 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
Agirre, M.; Vega, L. (20190821)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
Fanelli, L.; Krejcirik, D.; Vega, L. (20180628)We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the nonnegative semiaxis for all potentials satisfying a formsubordinate smallness condition. By developing ... 
Static and Dynamical, Fractional Uncertainty Principles
Kumar, S.; Ponce Vanegas, F.; Vega, L. (202103)We study the process of dispersion of lowregularity 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 selfadjointness of Dirac operators: Applications to the MIT bag model and deltashell interactions
OurmièresBonafos, T.; Vega, L. (20161221)We develop an approach to prove selfadjointness 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
Vega, L. (20150701)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 socalled binormal flow. The case of a regular polygon ... 
The initial value problem for the binormal flow with rough data
Banica, V.; Vega, L. (20151231)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
De la Hoz, F.; Vega, L. (20150801)In this paper, we consider the evolution of the socalled 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
Fernández Bertolin, A.; Vega, L. (20170325)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 ...