Browsing Linear and Non-Linear Waves by Title
Now showing items 17-36 of 120
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Carleman type inequalities for fractional relativistic operators
(2019-09-22)In this paper, we derive Carleman estimates for the fractional relativistic operator. Firstly, we consider changing-sign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity ... -
Control of pseudodifferential operators by maximal functions via weighted inequalities
(2019-01-01)We establish general weighted L 2 inequalities for pseudodifferential operators associated to the Hörmander symbol classes S ρ,δm . Such inequalities allow one to control these operators by fractional “non-tangential” ... -
Dirac Operators and Shell Interactions: A Survey
(2021-01-01)In this survey we gather recent results on Dirac operators coupled with δ-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterwards we switch to ... -
Discrepancy of Minimal Riesz Energy Points
(2021-12-01)We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz s-energy on the sphere Sd. Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished ... -
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 ... -
Eigenvalue Curves for Generalized MIT Bag Models
(2021)We study spectral properties of Dirac operators on bounded domains Ω ⊂ R 3 with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter τ ∈ R; the case τ = 0 corresponds to the MIT ... -
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. ... -
ENERGY CONSERVATION FOR 2D EULER WITH VORTICITY IN L(log L)α*
(2022-01-01)In these notes we discuss the conservation of the energy for weak solutions of the twodimensional incompressible Euler equations. Weak solutions with vorticity in (Formula presented) with p > 3/2 are always conservative, ... -
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
(2020-06-01)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 ... -
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. ... -
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 ... -
A Fefferman-Stein inequality for the Carleson operator
(2018-01-01)We provide a Fefferman-Stein type weighted inequality for maximally modulated Calderón-Zygmund operators that satisfy a priori weak type unweighted estimates. This inequality corresponds to a maximally modulated version ... -
The Frisch–Parisi formalism for fluctuations of the Schrödinger equation
(2022)We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, \delta}(t)$ be the fluctuations in time of $\int\lvert x \rvert^{2\delta}\lvert ... -
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 ...