Recent Submissions

  • Bilinear representation theorem 

    Li K.; Martikainen H.; Ou Y.; Vuorinen E. (Transactions of the American Mathematical Society, 2018-01-01)
    We represent a general bilinear Calderón--Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so ...
  • 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 ...
  • Improved A1 − A∞ and related estimates for commutators of rough singular integrals 

    Rivera-Ríos I.P. (Proceedings of the Edinburgh Mathematical Society, 2017)
    An $A_1-A_\infty$ estimate improving a previous result in [22] for $[b, T_\Omega]$ with $\Omega\in L^\infty(S^{n-1})$ and $b\in BMO$ is obtained. Also a new result in terms of the $A_\infty$ constant and the one ...
  • On a hyperbolic system arising in liquid crystal modelling 

    Fereisl E.; Rocca E.; Schimperna G.; Zarnescu A. (Journal of Hyperbolic Differential Equations, 2017-11)
    We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution ...
  • 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 ...
  • Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals 

    de Anna F.; Zarnescu A. (Journal of Differential Equations, 2017-10-02)
    We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law ...
  • Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$ 

    Mas A; Pizzichillo F. (Analysis & PDE, 2017-11)
    Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable re-scaling of $\mathbf{V}$, converges in the strong resolvent sense ...
  • Asymptotic behaviour for fractional diffusion-convection equations 

    Ignat L.; Stan D. (2017-10)
    We consider a convection-diffusion model with linear fractional diffusion in the sub-critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective ...
  • Existence of weak solutions for a general porous medium equation with nonlocal pressure 

    Stan D.; del Teso F.; Vázquez JL. (submitted, 2017-10)
    We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters ...
  • 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 ...
  • 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 ...
  • Weighted mixed weak-type inequalities for multilinear operators 

    Li K.; Ombrosi S.; Picardi B. (Studia Mathematica, 2017)
    In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main ...
  • Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions 

    Boggarapu P.; Roncal L.; Thangavelu S. (Transactions of the American Mathematical Society, 2017)
    Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the Dunkl--Hermite operator ...
  • Dispersive effects of weakly compressible and fast rotating inviscid fluids 

    Ngo V.-S; Scrobogna S. (Discrete and Continuous Dynamical Systems - Series A, 2017-08)
    We consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space $\mathbb{R}^3$, with initial data belonging to $ H^s \left( \mathbb{R}^3 \right), s>5/2 $. ...
  • On pointwise and weighted estimates for commutators of Calderón-Zygmund operators 

    Lerner A. K; Ombrosi S.; Rivera-Ríos I.P. (Advances in Mathematics, 2017)
    In recent years, it has been well understood that a Calderón-Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar ...
  • Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators 

    Hytönen T.; Li K. (Proceedings of the American Mathematical Society, 2017-07)
    We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p} ...
  • The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation 

    Mas A.; Pizzichillo F. (Journal of Mathematical Physics, 2017-08-03)
    This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by ...
  • Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity 

    Scrobogna S. (Revista Matemática Iberoamericana, 2017-07)
    We prove that the three-dimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero ...
  • 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 ...
  • Derivation of limit equation for a singular perturbation of a 3D periodic Boussinesq system 

    Scrobogna S. (Discrete and Continuous Dynamical Systems - Series A, 2017-07-15)
    We consider a system describing the dynamics of an hydrodynamical, density-dependent flow under the effects of gravitational forces. We prove that if the Froude number is sufficiently small such system is globally well ...

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