Browsing Linear and Non-Linear Waves by Title
Now showing items 21-40 of 55
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Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions
(IEEE Transactions on Magnetics, 2015-12-31)In this paper, we present a mean-field model of the spin-magnetization coupling in ferromagnetic materials. The model includes non-isotropic diffusion for spin dynamics, which is crucial in capturing strong spin-magnetization ... -
Modeling cardiac structural heterogeneity via space-fractional differential equations
(Computational and Mathematical Biomedical Engineering (CMBE2017) Proceedings, 2017)We discuss here the use of non-local 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, 2017-07-18)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, 2016-06-30)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
(2018-07-12)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ... -
On the regularity of solutions to the k-generalized korteweg-de vries equation
(Proceedings of the American Mathematical Society, 2018-07)This work is concerned with special regularity properties of solutions to the k-generalized Korteweg-de Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ... -
On the Relationship between the One-Corner Problem and the $M-$Corner Problem for the Vortex Filament Equation
(Journal of Nonlinear Science, 2018-06-28)In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular M-corner polygon as initial datum can be explained at infinitesimal times as the superposition of M one-corner initial ... -
Reconstruction from boundary measurements for less regular conductivities
(2016-10-01)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 ... -
Regularity of fractional maximal functions through Fourier multipliers
(2018)We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n \geq 2$. We also show that the spherical fractional maximal function ... -
Relativistic Hardy Inequalities in Magnetic Fields
(Journal of Statistical Physics, 2014-12-31)We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality ... -
The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation
(Journal of Mathematical Physics, 2017-08-03)This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by ... -
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments
(SIAM Journal on Numerical Analysis, 2018)\noindent We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t) \qquad\text{in}\qquad ... -
Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
(Letters in Mathematical Physics, 2018)We describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, ... -
Sharp bounds for the ratio of modified Bessel functions
(Mediterranean Journal of Mathematics, 2017-06-21)Let $I_{\nu }\left( x\right) $ be the modified Bessel functions of the first kind of order $\nu $, and $S_{p,\nu }\left( x\right) =W_{\nu }\left( x\right) ^{2}-2pW_{\nu }\left( x\right) -x^{2}$ with $W_{\nu }\left( x\right) ... -
Sharp exponential localization for eigenfunctions of the Dirac Operator
(2018)We determine the fastest possible rate of exponential decay at infinity for eigenfunctions of the Dirac operator $\mathcal D_n + \mathbb V$, being $\mathcal D_n$ the massless Dirac operator in dimensions $n=2,3$ and ... -
Shell interactions for Dirac operators: On the point spectrum and the confinement
(SIAM Journal on Mathematical Analysis, 2015-12-31)Spectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$ and $V$ is a measure-valued potential. The ... -
Singular Perturbation of the Dirac Hamiltonian
(2017-12-15)This thesis is devoted to the study of the Dirac Hamiltonian perturbed by delta-type potentials and Coulomb-type potentials. We analysed the delta-shell interaction on bounded and smooth domains and its approximation by ... -
Singularity formation for the 1-D cubic NLS and the Schrödinger map on $\mathbb{S}^2$
(2017-02-02)In this note we consider the 1-D cubic Schrödinger equation with data given as small perturbations of a Dirac-$\delta$ function and some other related equations. We first recall that although the problem for this type of ... -
Some remarks on the $L^p$ regularity of second derivatives of solutions to non-divergence elliptic equations and the Dini condition
(Rendiconti Lincei - Matematica e Applicazioni, 2017-05-30)In this note we prove an end-point regularity result on the $L^P$ integrability of the second derivatives of solutions to non-divergence form uniformly elliptic equations whose second derivatives are a priori only known ... -
Sparse bounds for pseudodifferential operators
(Journal d'Analyse Mathématique, 2018)We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of ...