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Now showing items 1-10 of 14

#### 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 ...

#### Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation

(2018-07-06)

We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. ...

#### On the regularity of solutions to the k-generalized korteweg-de vries equation

(Proceedings of the American Mathematical Society, 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 Relationship between the One-Corner Problem and the $M-$Corner Problem for the Vortex Filament Equation

(Journal of Nonlinear Science, 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 ...

#### Spectral stability of Schrödinger operators with subordinated complex potentials

(Journal of Spectral Theory, 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 ...

#### Variable Lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities

(Nonlinear Analysis, 2018-02-15)

We prove global Calder\'on-Zygmund type estimate in Lorentz spaces for variable power of the gradients to weak solution of nonlinear elliptic equations in a non-smooth domain. We mainly assume that the nonlinearities are ...

#### Weghted Lorentz and Lorentz-Morrey estimates to viscosity solutions of fully nonlinear elliptic equations

(Complex Variables and Elliptic Equations, 2018)

We prove a global weighted Lorentz and Lorentz-Morrey estimates of the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equation $F(D^{2}u,x)=f(x)$ defined in a bounded $C^{1,1}$ domain. The ...

#### Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials

(Letters in Mathematical Physics, 2018)

We describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, ...

#### Sharp exponential localization for eigenfunctions of the Dirac Operator

(2018)

We determine the fastest possible rate of exponential decay at
infinity for eigenfunctions of the Dirac operator $\mathcal D_n + \mathbb V$, being
$\mathcal D_n$ the massless Dirac operator in dimensions $n=2,3$ and ...

#### Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds

(2018)

The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian ...