Browsing Linear and NonLinear Waves by Title
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Discreteness of transmission eigenvalues for higherorder main terms and perturbations
(SIAM Journal on Mathematical Analysis, 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 ... 
An efficient multigrid strategy for largescale molecular mechanics optimization
(Journal of Computational Physics, 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
(TEMat, 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 ... 
Erratum to: Relativistic Hardy Inequalities in Magnetic Fields [J Stat Phys, 154, (2014), 866876, DOI 10.1007/s1095501409150]
(Journal of Statistical Physics, 20151231)[No abstract available] 
Existence of weak solutions for a general porous medium equation with nonlocal pressure
(submitted, 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 ... 
Gaussian Decay of Harmonic Oscillators and related models
(Journal of Mathematical Analysis and Applications, 20170515)We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can ... 
Hardy uncertainty principle, convexity and parabolic evolutions
(Communications in Mathematical Physics, 20160901)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 logconvexity properties and the derivation of ... 
HartreeFock theory with a selfgenerated magnetic field
(Journal of Mathematical Physics, 20170601)We prove the existence of a ground state within the HartreeFock theory for atoms and molecules, in the presence of selfgenerated magnetic fields, with and without direct spin coupling. The ground state exists provided ... 
Klein's Paradox and the Relativistic $\delta$shell Interaction in $\mathbb{R}^3$
(Analysis & PDE, 201711)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 rescaling of $\mathbf{V}$, converges in the strong resolvent sense ... 
Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
(Mathematische Nachrichten, 20170620)We prove a global Lorentz estimate of the Hessian of strong solutions to the CauchyDirichlet 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 ... 
Meanfield dynamics of the spinmagnetization coupling in ferromagnetic materials: Application to currentdriven domain wall motions
(IEEE Transactions on Magnetics, 20151231)In this paper, we present a meanfield model of the spinmagnetization coupling in ferromagnetic materials. The model includes nonisotropic diffusion for spin dynamics, which is crucial in capturing strong spinmagnetization ... 
Modeling cardiac structural heterogeneity via spacefractional differential equations
(Computational and Mathematical Biomedical Engineering (CMBE2017) Proceedings, 2017)We discuss here the use of nonlocal models in space and fractional order operators in the characterisation of structural complexity and the modeling of propagation in heterogeneous biological tissues. In the specific, we ... 
Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications
(Mathematical Inequalities & Applications, 20170718)Let $I_{v}\left( x\right) $ be modified Bessel functions of the first kind. We prove the monotonicity property of the function $x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ... 
On the bound states of Schrödinger operators with $\delta$interactions on conical surfaces
(Communications in Partial Differential Equations, 20160630)In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ... 
On the improvement of the Hardy inequality due to singular magnetic fields
(20180712)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the AharonovBohm field in all dimensions and establish a sharp Hardytype ... 
On the regularity of solutions to the kgeneralized kortewegde vries equation
(Proceedings of the American Mathematical Society, 201807)This work is concerned with special regularity properties of solutions to the kgeneralized Kortewegde Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ... 
On the Relationship between the OneCorner Problem and the $M$Corner Problem for the Vortex Filament Equation
(Journal of Nonlinear Science, 20180628)In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular Mcorner polygon as initial datum can be explained at infinitesimal times as the superposition of M onecorner initial ... 
Reconstruction from boundary measurements for less regular conductivities
(20161001)In this paper, following Nachman's idea [14] and Haberman and Tataru's idea [9], we reconstruct $C^1$ conductivity $\gamma$ or Lipchitz conductivity $\gamma$ with small enough value of $\nabla log\gamma$ in a Lipschitz ...