Browsing Linear and NonLinear Waves by Title
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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 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 improvement of the Hardy inequality due to singular magnetic fields
(20200901)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
(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
(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 ... 
On the smallness condition in linear inviscid damping: monotonicity and resonance chains
(2020)We consider the effects of mixing by smooth bilipschitz shear flows in the linearized Euler equations on $\mathbb{T}_{L}\times\mathbb{R}$. Here, we construct a model which is closely related to a small high frequency ... 
On the unique continuation of solutions to nonlocal nonlinear dispersive equations
(20200802)We prove unique continuation properties of solutions to a large class of nonlinear, nonlocal dispersive equations. The goal is to show that if (Formula presented.) are two suitable solutions of the equation defined in ... 
Pseudospectral Methods for the Fractional Laplacian on R
(20200702)In this thesis, first, we propose a novel pseudospectral method to approximate accu rately and efficiently the fractional Laplacian without using truncation. More pre cisely, given a bounded regular function defined over ... 
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 ... 
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
(20141231)We deal with Dirac operators with external homogeneous magnetic fields. Hardytype 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
(20170803)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 ... 
Riemann's nondifferentiable function and the binormal curvature flow
(20200714)We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object ... 
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory
(2019)Abstract. We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations ∂tu − Lσ,μ[φ(u)] = f(x,t) in RN × (0,T), where Lσ,μ is a general ... 
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments
(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 ... 
The Schrödinger equation and Uncertainty Principles
(202009)The main task of this thesis is the analysis of the initial data u0 of Schrödinger’s initial value problem in order to determine certain properties of its dynamical evolution. First we consider the elliptic Schrödinger ... 
SelfAdjoint Extensions for the Dirac Operator with CoulombType Spherically Symmetric Potentials
(2018)We describe the selfadjoint realizations of the operator $H:=i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)= x^{1} ( \nu \mathbb{I}_4 +\mu \beta i \lambda \alpha\cdot{x}/{x}\,\beta)$, ... 
Selfsimilar dynamics for the modified Kortewegde Vries equation
(20190409)We prove a local well posedness result for the modified Kortewegde Vries equa tion in a critical space designed so that is contains selfsimilar solutions. As a consequence, we can study the flow of this equation around ... 
Sensitivity of twin boundary movement to sample orientation and magnetic field direction in NiMnGa
(2019)When applying a magnetic field parallel or perpendicular to the long edge of a parallelepiped Ni MnGa stick, twin boundaries move instantaneously or gradullay through the sample. We evaluate the sample shape dependence ... 
Sharp bounds for the ratio of modified Bessel functions
(20170621)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) ...