• 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 ...

• Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds 

  Beltran D.; Hickman J.; Sogge C. D. (2018)

  The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian ...

• 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 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 ...

• On the Relationship between the One-Corner Problem and the $M-$Corner Problem for the Vortex Filament Equation 

  De la Hoz F.; Vega L. (Journal of Nonlinear Science, 2018-06-28)

  In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular M-corner polygon as initial datum can be explained at infinitesimal times as the superposition of M one-corner initial ...

• 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 ...

• On Bloom type estimates for iterated commutators of fractional integrals 

  Accomazzo N.; Martínez-Perales J.C.; Rivera-Ríos I.P. (Indiana University Mathematics Journal, 2018-04)

  In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. We give new proofs for those inequalities relying upon a new sparse ...

• 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 $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, ...

• 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 ...

• Variable Lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities 

  Liang S.; Zheng S. (Nonlinear Analysis, 2018-02-15)

  We prove global Calder\'on-Zygmund type estimate in Lorentz spaces for variable power of the gradients to weak solution of nonlinear elliptic equations in a non-smooth domain. We mainly assume that the nonlinearities are ...

• Zero limit of entropic relaxation time for the Shliomis model of ferrofluids 

  Scrobogna S. (2018-02-11)

  We construct solutions for the Shilomis model of ferrofluids in a critical space, uniformly in the entropic relaxation time $ \tau \in (0, \tau_0) $. This allows us to study the convergence when $ \tau\to 0 $ for such solutions.

• Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients 

  Zheng S.; Tian H. (Boundary Value Problems, 2017)

  We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the ...

• Weghted Lorentz and Lorentz-Morrey estimates to viscosity solutions of fully nonlinear elliptic equations 

  Junjie Zhang,Shenzhou Zheng (Complex Variables and Elliptic Equations, 2018)

  We prove a global weighted Lorentz and Lorentz-Morrey estimates of the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equation $F(D^{2}u,x)=f(x)$ defined in a bounded $C^{1,1}$ domain. The ...

• 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 ...

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