### Recent Submissions

• #### Bilinear representation theorem ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 $\mathbb{R}^3$ ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(Proceedings of the American Mathematical Society, 2017-07)
• #### Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity ﻿

(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 ﻿

(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 ﻿

(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 ...