Now showing items 38-57 of 61

    • Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials 

      Cassano B.; Pizzichillo F. (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 

      Zheng S.; Yang Z-H. (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 

      Cassano B. (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 

      Arrizabalaga N.; Mas A.; Vega L. (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 

      Pizzichillo F. (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 $\mathbb{S}^2$ 

      Banica V.; Vega L. (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 

      Eceizabarrena D. (Comptes Rendus Mathematique, 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 remarks on the $L^p$ regularity of second derivatives of solutions to non-divergence elliptic equations and the Dini condition 

      Escauriaza L.; Montaner S. (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 

      Beltran D.; Cladek L. (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 ...
    • Spectral asymptotics for $\delta$-interactions on sharp cones 

      Ourmières-Bonafos T.; Pankrashkin K.; Pizzichillo F. (Journal of Mathematical Analysis and Applications, 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 

      Dauge M.; Ourmières-Bonafos T.; Raymond N. (Communications on Pure and Applied Analysis, 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 

      Fanelli L.; Krejcirik D.; Vega L. (Journal of Spectral Theory, 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 

      Krejčiřík D.; Lotoreichik V.; Ourmières-Bonafos T. (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 ...
    • A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions 

      Ourmières-Bonafos T.; Vega L. (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 

      Vega L. (Communications on Pure and Applied Analysis (CPAA), 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 

      Banica V.; Vega L. (Annales Scientifiques de l'Ecole Normale Superieure, 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 

      de La Hoz F.; Vega L. (Acta Applicandae Mathematicae, 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 

      Nós R.L.; Roma A. M.; Garcia-Cervera C.J.; Ceniceros H.D. (Journal of Non-Newtonian Fluid Mechanics, 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 

      Del Teso F.; Endal J.; Jacobsen E.R. (Advances in Mathematics, 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 

      Fernández Bertolin A.; Vega L. (Journal of Functional Analysis, 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 ...