Now showing items 68-87 of 119

    • Partial regularity and smooth topology-preserving approximations of rough domains 

      Ball J.M.; Zarnescu A. (Calculus of Variations and Partial Differential Equations, 2017-01-01)
      For a bounded domain $\Omega\subset\mathbb{R}^m, m\geq 2,$ of class $C^0$, the properties are studied of fields of `good directions', that is the directions with respect to which $\partial\Omega$ can be locally represented ...
    • Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates 

      Li K.; Ombrosi S.; Pérez C. (Mathematische Annalen, 2018-09)
      We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that $$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, ...
    • A quantitative approach to weighted Carleson condition 

      Rivera-Ríos I.P. (Concrete Operators, 2017-05-05)
      Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator \[ \mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0 \] are ...
    • Quantitative weighted estimates for rough homogeneous singular integrals 

      Hytönen T. P.; Roncal L.; Tapiola O. (Israel Journal of Mathematics, 2017-03-11)
      We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space $L^2(w)$, we obtain a bound ...
    • Quantitative weighted estimates for singular integrals and commutators 

      Rivera-Ríos I.P. (2018-02-27)
      In this dissertation several quantitative weighted estimates for singular integral op- erators, commutators and some vector valued extensions are obtained. In particular strong and weak type $(p, p)$ estimates, Coifman-Fe ...
    • 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 ...
    • Reconstruction from boundary measurements for less regular conductivities 

      García A.; Zhang G. (2016-10-01)
      In this paper, following Nachman's idea [14] and Haberman and Tataru's idea [9], we reconstruct $C^1$ conductivity $\gamma$ or Lipchitz conductivity $\gamma$ with small enough value of $|\nabla log\gamma|$ in a Lipschitz ...
    • Regularity of fractional maximal functions through Fourier multipliers 

      Beltran D.; Ramos J. P.; Saari O. (2018)
      We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n \geq 2$. We also show that the spherical fractional maximal function ...
    • 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 ...
    • 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 ...
    • 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 ...
    • Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments 

      Del Teso F.; Endal J.; Jakobsen E.R. (SIAM Journal on Numerical Analysis, 2018)
      \noindent We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t) \qquad\text{in}\qquad ...
    • 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 ...
    • 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 ...