Browsing Linear and Non-Linear Waves by Title
Now showing items 83-102 of 120
-
The Schrödinger equation and Uncertainty Principles
(2020-09)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 ... -
Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
(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 $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, ... -
Self-adjointness of two-dimensional Dirac operators on corner domains
(2021-01-01)We investigate the self-adjointness of the two-dimensional Dirac operator D, with quantum-dot and Lorentz-scalar i-shell boundary conditions, on piecewise C2 domains (with finitely many corners). For both models, we prove ... -
Self-similar dynamics for the modified Korteweg-de Vries equation
(2019-04-09)We prove a local well posedness result for the modified Korteweg-de Vries equa- tion in a critical space designed so that is contains self-similar 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 Ni-Mn-Ga
(2019)When applying a magnetic field parallel or perpendicular to the long edge of a parallelepiped Ni- Mn-Ga 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
(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 ... -
Sharp local smoothing estimates for Fourier integral operators
(2019)The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which ... -
A sharp lorentz-invariant strichartz norm expansion for the cubic wave equation in \mathbb{R}^{1+3}
(2020)We provide an asymptotic formula for the maximal Stri- chartz norm of small solutions to the cubic wave equation in Minkowski space. The leading coefficient is given by Foschi’s sharp constant for the linear Strichartz ... -
Shell interactions for Dirac operators: On the point spectrum and the confinement
(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 geometric properties of Riemann’s non-differentiable function
(2019-11-06)Riemann’s non-differentiable function is a celebrated example of a continuous but almost nowhere differentiable function. There is strong numeric evidence that one of its complex versions represents a geometric trajectory ... -
Some lower bounds for solutions of Schrodinger evolutions
(2019-08-21)We present some lower bounds for regular solutions of Schr odinger equations with bounded and time dependent complex potentials. Assuming that the solution has some positive mass at time zero within a ball of certain radius, ... -
Some remarks on the $L^p$ regularity of second derivatives of solutions to non-divergence elliptic equations and the Dini condition
(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
(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 ... -
Spectral asymptotics for $\delta$-interactions on sharp cones
(2017)We investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ... -
Spectral asymptotics of the Dirichlet Laplacian in a conical layer
(2015-05-01)The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture limit. On the one hand, we prove that, for ... -
Spectral stability of Schrödinger operators with subordinated complex potentials
(2018-06-28)We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness condition. By developing ... -
Spectral Transitions for Aharonov-Bohm Laplacians on Conical Layers
(2016-07-11)We consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an Aharonov-Bohm magnetic field supported on the axis of symmetry and Dirichlet boundary conditions on the boundary ...