Now showing items 29-48 of 88

• #### Hardy uncertainty principle, convexity and parabolic evolutions ﻿

(2016-09-01)
We give a new proof of the $L^2$ version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of ...
• #### 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: ...
• #### Hartree-Fock theory with a self-generated magnetic field ﻿

(2017-06-01)
We prove the existence of a ground state within the Hartree-Fock theory for atoms and molecules, in the presence of self-generated magnetic fields, with and without direct spin coupling. The ground state exists provided ...
• #### Hypocoercivity of linear kinetic equations via Harris's Theorem ﻿

(2019-02-27)
We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus $(x,v) \in \mathbb{T}^d \times \mathbb{R}^d$ or on the whole ...
• #### Invariant measures for the dnls equation ﻿

(2020-10-02)
We describe invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schr\"odinger equation (DNLS) constructed in \cite{MR3518561, Genovese2018}. The construction works for small $L^2$ ...
• #### Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$ ﻿

(2017-11)
Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable re-scaling of $\mathbf{V}$, converges in the strong resolvent sense ...
• #### Lorentz estimates for asymptotically regular fully nonlinear parabolic equations ﻿

(2017-06-20)
We prove a global Lorentz estimate of the Hessian of strong solutions to the Cauchy-Dirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ ...
• #### Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients ﻿

(2017)
We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the ...
• #### Magnetic domain-twin boundary interactions in Ni-Mn-Ga ﻿

(2020-04)
The stress required for the propagation of twin boundaries in a sample with fine twins increases monotonically with ongoing deformation. In contrast, for samples with a single twin boundary, the stress exhibits a plateau ...
• #### Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions ﻿

(2015-12-31)
In this paper, we present a mean-field model of the spin-magnetization coupling in ferromagnetic materials. The model includes non-isotropic diffusion for spin dynamics, which is crucial in capturing strong spin-magnetization ...
• #### Modeling cardiac structural heterogeneity via space-fractional differential equations ﻿

(2017)
We discuss here the use of non-local models in space and fractional order operators in the characterisation of structural complexity and the modeling of propagation in heterogeneous biological tissues. In the specific, we ...
• #### Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications ﻿

(2017-07-18)
Let $I_{v}\left( x\right)$ be modified Bessel functions of the first kind. We prove the monotonicity property of the function $x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ... • #### On the bound states of Schrödinger operators with$\delta$-interactions on conical surfaces ﻿ (2016-06-30) In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a$\delta$-interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ... • #### On the energy of critical solutions of the binormal flow ﻿ (2019-07-20) The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisen- berg model in ferromagnetism, and the 1-D cubic Schr ... • #### On the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsion ﻿ (2019-09-03) In this paper, we consider the evolution of the Vortex Filament equa- tion (VFE): Xt = Xs ∧ Xss, taking M-sided regular polygons with nonzero torsion as initial data. Us- ing algebraic techniques, backed by numerical ... • #### On the improvement of the Hardy inequality due to singular magnetic fields ﻿ (2018-07-12) We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ... • #### On the improvement of the Hardy inequality due to singular magnetic fields ﻿ (2018-07-12) We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ... • #### On the regularity of solutions to the k-generalized korteweg-de vries equation ﻿ (2018-07) This work is concerned with special regularity properties of solutions to the k-generalized Korteweg-de Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ... • #### On the Relationship between the One-Corner Problem and the$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 ...