Now showing items 84-103 of 120

    • Sharp weighted estimates involving one supremum 

      Li K. (Comptes Rendus Mathematique, 2017-07)
      In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular ...
    • Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals 

      Murza A.C.; Teruel A.E.; Zarnescu A. (Proceedings of the Royal Society A-Mathematical, Physical and Engineering Sciences, 2018-02-14)
      We consider the Beris-Edwards model describing nematic liquid crystal dynamics and restrict to a shear flow and spatially homogeneous situation. We analyze the dynamics focusing on the effect of the flow. We show that in ...
    • 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 remark on the existence of infinitely many nonphysical solutions to the incompressible Navier-Stokes equations 

      Scrobogna S. (Journal of Mathematical Analysis and Applications, 2018-10)
      We prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible Navier-Stokes equations in $ \mathbb{R}^2 $ and Burgers equation in $\mathbb{R} $ with vanishing ...
    • 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 maximal rough singular integrals via the Fourier transform 

      Di Plinio F.; Hytönen T.; Li K. (Annales de l'institut Fourier, 2019-03-12)
      We prove a quantified sparse bound for the maximal truncations of convolution-type singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by Conde-Alonso, Culiuc, ...
    • 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 ...
    • Sparse domination theorem for multilinear singular integral operators with $L^{r}$-Hörmander condition 

      Li K. (Michigan Mathematical Journal, 2017-04-01)
      In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the so-called multilinear $L^{r}$-Hörmander condition, then $T$ can be dominated by multilinear sparse operators.
    • 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 ...
    • Sphere-valued harmonic maps with surface energy and the K13 problem 

      Day S.; Zarnescu A. (Advances in the Calculus of Variations, 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 ...
    • 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 Observations on Commutators of Singular Integral Operators with BMO Functions 

      Pérez C.; Rivera-Ríos I.P. (AWM-Springer Series, Harmonic Analysis, Partial Differentail Equations, Complex Analysis, Banach Spaces, and Operator Theory, 2016-07-01)
      Three observations on commutators of Singular Integral Operators with BMO functions are exposed, namely 1 - The already known subgaussian local decay for the commutator, namely $\[\frac{1}{|Q|}\left|\left\{x\in Q\, : ...