Browsing Linear and NonLinear Waves by Title
Now showing items 928 of 61

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 ... 
Boundary Triples for the Dirac Operator with CoulombType Spherically Symmetric Perturbations
(Journal of Mathematical Physics, 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 ... 
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 ... 
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. ... 
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 ... 
A Hardytype inequality and some spectral characterizations for the Dirac–Coulomb operator
(Revista Matemática Complutense, 201906)We prove a sharp Hardytype inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrixvalued potentials $\mathbf V$ of Coulomb type: ... 
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 ... 
Hypocoercivity of linear kinetic equations via Harris's Theorem
(Kinetic & Related Models, 20190227)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 ... 
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) ...