Now showing items 1-20 of 97

    • Relativistic Hardy Inequalities in Magnetic Fields 

      Fanelli L.; Vega L.; Visciglia N. (Journal of Statistical Physics, 2014-12-31)
      We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality ...
    • Vortex filament equation for a regular polygon 

      de La Hoz F.; Vega L. (Nonlinearity, 2014-12-31)
      In this paper, we study the evolution of the vortex filament equation,$$ X_t = X_s \wedge X_{ss},$$with $X(s, 0)$ being a regular planar polygon. Using algebraic techniques, supported by full numerical simulations, we give ...
    • 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 ...
    • 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 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 ...
    • 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 ...
    • An atomistic/continuum coupling method using enriched bases 

      Chen J.; Garcia-Cervera C.J.; Li X. (Multiscale Modeling and Simulation, 2015-12-31)
      A common observation from an atomistic to continuum coupling method is that the error is often generated and concentrated near the interface, where the two models are combined. In this paper, a new method is proposed to ...
    • Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions 

      Chen J.; Garcia-Cervera C.J.; Yang X. (IEEE Transactions on Magnetics, 2015-12-31)
      In this paper, we present a mean-field model of the spin-magnetization coupling in ferromagnetic materials. The model includes non-isotropic diffusion for spin dynamics, which is crucial in capturing strong spin-magnetization ...
    • 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 ...
    • Erratum to: Relativistic Hardy Inequalities in Magnetic Fields [J Stat Phys, 154, (2014), 866-876, DOI 10.1007/s10955-014-0915-0] 

      Fanelli L.; Vega L.; Visciglia N. (Journal of Statistical Physics, 2015-12-31)
      [No abstract available]
    • A Mean-field model for spin dynamics in multilayered ferromagnetic media 

      Chen J.; Garcia-Cervera C.J.; Yang X. (Multiscale Modeling and Simulation, 2015-12-31)
      In this paper, we develop a mean-field model for describing the dynamics of spintransfer torque in multilayered ferromagnetic media. Specifically, we use the techniques of Wigner transform and moment closure to connect the ...
    • Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer 

      Ombrosi S.; Pérez C. (Colloquium Mathematicum, 2016-01-01)
      In this paper we study mixed weighted weak-type inequal- ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2].
    • Global Uniqueness for The Calderón Problem with Lipschitz Conductivities 

      Caro P.; Rogers K.M. (Forum of Mathematics, Pi, 2016-01-01)
      We prove uniqueness for the Calderón problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three- and four-dimensional cases, this confirms a conjecture of ...
    • Inverse scattering for a random potential 

      Caro P.; Helin T.; Lassas M. (2016-05)
      In this paper we consider an inverse problem for the $n$-dimensional random Schrödinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a ...
    • An Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators 

      Arrizabalaga N.; Mas A.; Vega L. (Communications in Mathematical Physics, 2016-06-01)
      In this article we investigate spectral properties of the coupling $H + V_{\lambda}$, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$, $m>0$ and $V_{\lambda}$ is an electrostatic shell ...
    • Quantitative weighted mixed weak-type inequalities for classical operators 

      Ombrosi S.; Pérez C.; Recchi J. (Indiana University Mathematics Journal, 2016-06-30)
      We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calderón-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by ...
    • On the bound states of Schrödinger operators with $\delta$-interactions on conical surfaces 

      Lotoreichik V.; Ourmières-Bonafos T. (Communications in Partial Differential Equations, 2016-06-30)
      In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$-interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ...
    • Reverse Hölder Property for Strong Weights and General Measures 

      Luque T.; Pérez C.; Rela E. (Journal of Geometric Analysis, 2016-06-30)
      We present dimension-free reverse Hölder inequalities for strong $A^{\ast}_p$ weights, $1 \le p < \infty$. We also provide a proof for the full range of local integrability of $A^{\ast}_1$ weights. The common ingredient ...
    • 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\, : ...
    • A note on the off-diagonal Muckenhoupt-Wheeden conjecture 

      Cruz-Uribe D.; Martell J.M.; Pérez C. (WSPC Proceedings, 2016-07-01)
      We obtain the off-diagonal Muckenhoupt-Wheeden conjecture for Calderón-Zygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the Hardy-Littlewood maximal function satisfies the following ...