Now showing items 55-74 of 167

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

(Communications in Mathematical Physics, 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 ...
• #### Hardy-type inequalities for fractional powers of the Dunkl-Hermite operator ﻿

(Proc. Edinburgh Math. Soc. (2), 2018)
We prove Hardy-type inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use h-harmonic expansions to reduce the ...
• #### A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator ﻿

(Revista Matemática Complutense, 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 ﻿

(Revista Matemática Complutense, 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 ﻿

(Journal of Mathematical Physics, 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 ...
• #### Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity ﻿

(Revista Matemática Iberoamericana, 2017-07)
We prove that the three-dimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero ...
• #### Hölder-Lebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian ﻿

(Discrete Contin. Dyn. Syst., 2018)
We study the equations $\partial_t u(t,n) = L u(t,n) + f(u(t,n),n); \partial_t u(t,n) = iL u(t,n) + f(u(t,n),n)$ and $\partial_{tt} u(t,n) =Lu(t,n) + f(u(t,n),n)$, where $n\in \mathbb{Z}$, $t\in (0,\infty)$, and $L$ ...
• #### Hypocoercivity of linear kinetic equations via Harris's Theorem ﻿

(Kinetic & Related Models, 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 ...
• #### Improved A1 − A∞ and related estimates for commutators of rough singular integrals ﻿

(Proceedings of the Edinburgh Mathematical Society, 2017)
An $A_1-A_\infty$ estimate improving a previous result in [22] for $[b, T_\Omega]$ with $\Omega\in L^\infty(S^{n-1})$ and $b\in BMO$ is obtained. Also a new result in terms of the $A_\infty$ constant and the one ...
• #### Improved fractional Poincaré type inequalities in John domains ﻿

(Arkiv för Matematik, 2019)
We obtain improved fractional Poincaré inequalities in John domains of a metric space $(X, d)$ endowed with a doubling measure $\mu$ under some mild regularity conditions on the measure $\mu$. We also give sufficient ...
• #### Inverse scattering for a random potential ﻿

(2016-05)
In this paper we consider an inverse problem for the $n$-dimensional random Schrödinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a ...
• #### Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$ ﻿

(Analysis & PDE, 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 ...
• #### Landau-de Gennes Corrections to the Oseen-Frank Theory of Nematic Liquid Crystals ﻿

(Archive for Rational Mechanics and Analysis, 2020-01-03)
We study the asymptotic behavior of the minimisers of the Landau-de Gennes model for nematic liquid crystals in a two-dimensional domain in the regime of small elastic constant. At leading order in the elasticity constant, ...
• #### Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the one-constant approximation ﻿

(Mathematical Models and Methods in Applied Sciences, 2016-12-31)
We consider the two-dimensional Landau-de Gennes energy with several elastic constants, subject to general $k$-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent ...
• #### Lorentz estimates for asymptotically regular fully nonlinear parabolic equations ﻿

(Mathematische Nachrichten, 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 ﻿

(Boundary Value Problems, 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 ...
• #### Maximal estimates for a generalized spherical mean Radon transform acting on radial functions ﻿

(Annali de Matematica Pura et Applicata, 2020)
We study a generalized spherical means operator, viz.\ generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local ...
• #### Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions ﻿

(IEEE Transactions on Magnetics, 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 ...
• #### Minimizers of a Landau-de Gennes energy with a subquadratic elastic energy ﻿

(Archive for Rational Mechanics and Analysis, 2019)
We study a modified Landau-de Gennes model for nematic liq- uid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional ...
• #### Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions ﻿

(Transactions of the American Mathematical Society, 2017)
Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the Dunkl--Hermite operator ...