Now showing items 85-104 of 110

• #### 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 ...
• #### Static and Dynamical, Fractional Uncertainty Principles ﻿

(2021-03)
We study the process of dispersion of low-regularity solutions to the Schrödinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get ...
• #### A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions ﻿

(2016-12-21)
We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a $C^2$-compact surface without boundary. To do so we are lead to study the layer potential induced by the ...
• #### The dynamics of vortex filaments with corners ﻿

(2015-07-01)
This paper focuses on surveying some recent results obtained by the author together with V. Banica on the evolution of a vortex filament with one corner according to the so-called binormal flow. The case of a regular polygon ...
• #### The initial value problem for the binormal flow with rough data ﻿

(2015-12-31)
In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove that under suitable conditions on the ...
• #### The Vortex Filament Equation as a Pseudorandom Generator ﻿

(2015-08-01)
In this paper, we consider the evolution of the so-called vortex filament equation (VFE), $$X_t = X_s \wedge X_{ss},$$ taking a planar regular polygon of M sides as initial datum. We study VFE from a completely novel ...
• #### Three-dimensional coarsening dynamics of a conserved, nematic liquid crystal-isotropic fluid mixture ﻿

(2017-09)
We present a numerical investigation of the three-dimensional coarsening dynamics of a nematic liquid crystal-isotropic fluid mixture using a conserved phase field model. The model is a coupled system for a generalized ...
• #### Uniqueness and Properties of Distributional Solutions of Nonlocal Equations of Porous Medium Type ﻿

(2016-09-01)
We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem for the anomalous diffusion equation $\partial_tu-\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ ...
• #### Uniqueness properties for discrete equations and Carleman estimates ﻿

(2017-03-25)
Using Carleman estimates, we give a lower bound for solutions to the discrete Schrödinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of ...
• #### Uniqueness properties of solutions to the Benjamin-Ono equation and related models ﻿

(2020-03-15)
We prove that if u1,u2 are real solutions of the Benjamin-Ono equation defined in (x,t)∈R×[0,T] which agree in an open set Ω⊂R×[0,T], then u1≡u2. We extend this uniqueness result to a general class of equations of Benjamin-Ono ...
• #### Uniqueness Properties of Solutions to the Benjamin-Ono equation and related models ﻿

(2019-01-31)
We prove that if u1, u2 are solutions of the Benjamin- Ono equation defined in (x, t) ∈ R × [0, T ] which agree in an open set Ω ⊂ R × [0,T], then u1 ≡ u2. We extend this uniqueness result to a general class of equations ...