Now showing items 17-36 of 98

• #### Discreteness of transmission eigenvalues for higher-order main terms and perturbations ﻿

(2016-07-01)
In this paper we extend Sylvester's approach via upper triangular compact operators to establish the discreteness of transmission eigenvalues for higher-order main terms and higher-order perturbations. The coefficients of ...
• #### Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions ﻿

(2017-04-28)
In this work, we propose novel discretisations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heat-semigroup formalism. Specifically, we combine suitable ...
• #### Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics ﻿

(2021-07-30)
In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to ...
• #### An efficient multigrid strategy for large-scale molecular mechanics optimization ﻿

(2017-08-01)
Static mechanical properties of materials require large-scale nonlinear optimization of the molecular mechanics model under various controls. This paper presents an efficient multigrid strategy to solve such problems. This ...
• #### El efecto de Talbot: de la óptica a la ecuación de Schrödinger ﻿

(2017-07)
El objetivo de este artículo es dar a conocer un bello efecto óptico que se denomina efecto de Talbot. Primero, describiremos el fenómeno y comentaremos su descubrimiento a mediados del siglo XIX. A continuación, analizaremos ...
• #### Endpoint Sobolev continuity of the fractional maximal function in higher dimensions ﻿

(2019)
We establish continuity mapping properties of the non-centered fractional maximal operator $M_{\beta}$ in the endpoint input space $W^{1,1}(\mathbb{R}^d)$ for $d \geq 2$ in the cases for which its boundedness is known. ...
• #### Erratum to: Relativistic Hardy Inequalities in Magnetic Fields [J Stat Phys, 154, (2014), 866-876, DOI 10.1007/s10955-014-0915-0] ﻿

(2015-12-31)
[No abstract available]
• #### Evolution of Polygonal Lines by the Binormal Flow ﻿

(2020-02-05)
The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr ̈odinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. ...
• #### Evolution of Polygonal Lines by the Binormal Flow ﻿

(2020-06-01)
The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schrödinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. Finally ...
• #### Exact Constructions in the (Non-linear) Planar Theory of Elasticity: From Elastic Crystals to Nematic Elastomers ﻿

(2020-07)
In this article we deduce necessary and sufficient conditions for the presence of “Conti-type”, highly symmetric, exactly stress-free constructions in the geometrically non-linear, planar n-well problem, generalising results ...
• #### Existence of weak solutions for a general porous medium equation with nonlocal pressure ﻿

(2017-10)
We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters ...
• #### Gaussian Decay of Harmonic Oscillators and related models ﻿

(2017-05-15)
We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0-order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can ...
• #### A geometric and physical study of Riemann's non-differentiable function ﻿

(2020-07-08)
Riemann's non-differentiable function is a classic example of a continuous but almost nowhere differentiable function, whose analytic regularity has been widely studied since it was proposed in the second half of the 19th ...
• #### Geometric differentiability of Riemann's non-differentiable function ﻿

(2020-06)
Riemann’s non-differentiable function is a classic example of a continuous function which is almost nowhere differentiable, and many results concerning its analytic regularity have been shown so far. However, it can also ...
• #### 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: ...
• #### 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 ...
• #### 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 ...