### Recent Submissions

• #### Flow with $A_\infty(\mathbb R)$ density and transport equation in $\mathrm{BMO}(\mathbb R)$ ﻿

(Forum of Mathematics, Sigma, 2019-11)
We show that, if $b\in L^1(0,T;L^1_{\rm {loc}}(\mathbb R))$ has spatial derivative in the John-Nirenberg space ${\rm{BMO}}(\mathbb R)$, then it generates a unique flow $\phi(t,\cdot)$ which has an $A_\infty(\mathbb R)$ ...
• #### Bilinear Calderón--Zygmund theory on product spaces ﻿

(Journal des Math\'ematiques Pures et Appliqu\'ees, 2019-10)
We develop a wide general theory of bilinear bi-parameter singular integrals $T$. This includes general Calder\'on--Zygmund type principles in the bilinear bi-parameter setting: easier bounds, like estimates in the Banach ...
• #### Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function ﻿

(Journal of Geometric Analysis, 2019-12)
We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping. Quantitative weighted estimates are obtained for this operator. ...
• #### An optimal scaling to computationally tractable dimensionless models: Study of latex particles morphology formation ﻿

(Computer Physics Communications, 2020-02)
In modelling of chemical, physical or biological systems it may occur that the coefficients, multiplying various terms in the equation of interest, differ greatly in magnitude, if a particular system of units is used. Such ...
• #### Some geometric properties of Riemann’s non-differentiable function ﻿

(Comptes Rendus Mathematique, 2019-11-06)
Riemann’s non-differentiable function is a celebrated example of a continuous but almost nowhere differentiable function. There is strong numeric evidence that one of its complex versions represents a geometric trajectory ...
• #### Models for damped water waves ﻿

(SIAM Journal of Applied Mathematics, 2019)
In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative ...
• #### Análisis de Fourier en el toro infinito-dimensional ﻿

(2019-10-24)
Se presentan algunos resultados originales de análisis armónico para funciones definidas en el toro infinito, que es el grupo topológico compacto consistente en el producto cartesiano de una familia numerable de toros ...
• #### Asymptotic behaviour of some nonlocal equations in mathematical biology and kinetic theory ﻿

(2019-09)
We study the long-time behaviour of solutions to some partial differential equations arising in modeling of several biological and physical phenomena. In this work, the type of the equations we consider is mainly nonlocal, ...
• #### Minimizers of a Landau-de Gennes energy with a subquadratic elastic energy ﻿

(Archive for Rational Mechanics and Analysis, 2019)
We study a modified Landau-de Gennes model for nematic liq- uid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional ...
• #### Reconstruction of the Derivative of the Conductivity at the Boundary ﻿

(2019-08)
We describe a method to reconstruct the conductivity and its normal derivative at the boundary from the knowledge of the potential and current measured at the boundary. This boundary determination implies the uniqueness ...
• #### A Bilinear Strategy for Calderón's Problem ﻿

(2019-08)
Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\'on's problem is to decide whether the ...
• #### $A_1$ theory of weights for rough homogeneous singular integrals and commutators ﻿

(Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V, 2019)
Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $\BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \|T_\Omega ...
• #### On the absolute divergence of Fourier series in the infinite dimensional torus ﻿

(Colloquium Mathematicum, 2019-03-22)