Browsing Linear and NonLinear Waves by Title
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Bayesian approach to inverse scattering with topological priors
(2020)We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite ... 
Bilinear identities involving the $k$plane transform and Fourier extension operators
(2019)We prove certain $L^2(\mathbb{R}^n)$ bilinear estimates for Fourier extension operators associated to spheres and hyperboloids under the action of the $k$plane transform. As the estimates are $L^2$based, they follow from ... 
Bilinear identities involving the kplane transform and Fourier extension operators
(20191130)We prove certain L2pRnq bilinear estimates for Fourier extension operators associ ated to spheres and hyperboloids under the action of the kplane transform. As the estimates are L2based, they follow from bilinear ... 
Boundary Triples for the Dirac Operator with CoulombType Spherically Symmetric Perturbations
(201902)We determine explicitly a boundary triple for the Dirac operator $H:=i\alpha\cdot \nabla + m\beta + \mathbb V(x)$ in $\mathbb R^3$, for $m\in\mathbb R$ and $\mathbb V(x)= x^{1} ( \nu \mathbb{I}_4 +\mu \beta i \lambda ... 
Carleman type inequalities for fractional relativistic operators
(20190922)In this paper, we derive Carleman estimates for the fractional relativistic operator. Firstly, we consider changingsign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity ... 
Dirac Operators and Shell Interactions: A Survey
(20210101)In this survey we gather recent results on Dirac operators coupled with δshell interactions. We start by discussing recent advances regarding the question of selfadjointness for these operators. Afterwards we switch to ... 
Discrepancy of Minimal Riesz Energy Points
(20211201)We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz senergy 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 Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished ...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 higherorder main terms and perturbations
(20160701)In this paper we extend Sylvester's approach via upper triangular compact operators to establish the discreteness of transmission eigenvalues for higherorder main terms and higherorder perturbations. The coefficients of ... 
Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions
(20170428)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 heatsemigroup formalism. Specifically, we combine suitable ... 
Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics
(20210730)In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevreytype spaces as time tends to infinity. Thus, echo chains are shown to ... 
An efficient multigrid strategy for largescale molecular mechanics optimization
(20170801)Static mechanical properties of materials require largescale 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
(201707)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 noncentered 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*
(20220101)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), 866876, DOI 10.1007/s1095501409150]
(20151231)[No abstract available] 
Evolution of Polygonal Lines by the Binormal Flow
(20200205)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
(20200601)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 (Nonlinear) Planar Theory of Elasticity: From Elastic Crystals to Nematic Elastomers
(202007)In this article we deduce necessary and sufficient conditions for the presence of “Contitype”, highly symmetric, exactly stressfree constructions in the geometrically nonlinear, planar nwell problem, generalising results ... 
Existence of weak solutions for a general porous medium equation with nonlocal pressure
(201710)We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m1}\nabla (\Delta)^{s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters ... 
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 ...