Now showing items 81-100 of 240

• #### 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 ...
• #### Hardy-type inequalities for fractional powers of the Dunkl-Hermite operator ﻿

(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 ﻿

(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: ...
• #### A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator ﻿

(2020-01-01)
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 ...
• #### 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 ...
• #### Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity ﻿

(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 regularity and convergence for a non-local model of nematic liquid crystals in the large-domain limit ﻿

(2022-02-01)
We consider a non-local free energy functional, modelling a competition between entropy and pairwise interactions reminiscent of the second order virial expansion, with applications to nematic liquid crystals as a particular ...
• #### Hölder-Lebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ...
• #### 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 $L^2$ ...
• #### 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 $\mathbb{R}^3$ ﻿

(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 ﻿

(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, ...
• #### Leaky Cell Model of Hard Spheres ﻿

(9-03-20)
We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e., the volume of space that a sphere can explore without ...
• #### Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the one-constant approximation ﻿

(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 ﻿

(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 ...