Now showing items 182-201 of 217

• #### 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 ...
• #### Sphere-valued harmonic maps with surface energy and the K13 problem ﻿

(2017-11)
We consider an energy functional motivated by the celebrated K13 problem in the Oseen-Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an ...
• #### 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 ...
• #### Symmetry and Multiplicity of Solutions in a Two-Dimensional Landau–de Gennes Model for Liquid Crystals ﻿

(2020-05-20)
We consider a variational two-dimensional Landau–de Gennes model in the theory of nematic liquid crystals in a disk of radius R. We prove that under a symmetric boundary condition carrying a topological defect of degree ...
• #### 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 Observations on Commutators of Singular Integral Operators with BMO Functions ﻿

(2016-07-01)
• #### Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7 ﻿

(2018-09-01)
For ε>0, we consider the Ginzburg-Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, we prove that for every ε>0, there exists a unique global ...
• #### 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 ...