Analysis of Partial Differential Equations (APDE)
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Various results concerning homogenisation of nematic liquid crystals
(20221017)In this thesis we present various results concerning homogenisation of nematic liquid crystals: two of them are in perforated domains, while the other one concerns rates of convergence for boundary homogenisation. The first ... 
Motion of a rigid body in a compressible fluid with Navierslip boundary condition
(20221125)In this work, we study the motion of a rigid body in a bounded domain which is filled with a compressible isentropic fluid. We consider the Navierslip boundary condition at the interface as well as at the boundary of the ... 
Sharp local smoothing estimates for Fourier integral operators
(2019)The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which ... 
A∞ condition for general bases revisited: complete classification of definitions
(20220527)We refer to the discussion on different characterizations of the A∞ class of weights, initiated by Duoandikoetxea, MartínReyes, and Ombrosi [Math. Z. 282 (2016), pp. 955–972]. Twelve definitions of the A∞ condition ... 
Corrigendum to: An extension problem and trace Hardy inequality for the sublaplacian on Htype groups
(20210310)Recently we have found a couple of errors in our paper entitled An extension problem and trace Hardy inequality for the subLaplacian on $H$type groups, Int. Math. Res. Not. IMRN (2020), no. 14, 42384294. They concern ... 
ENERGY CONSERVATION FOR 2D EULER WITH VORTICITY IN L(log L)α*
(20220101)In these notes we discuss the conservation of the energy for weak solutions of the twodimensional incompressible Euler equations. Weak solutions with vorticity in (Formula presented) with p > 3/2 are always conservative, ... 
Existence of a weak solution to a nonlinear fluidstructure interaction problem with heat exchange
(20220101)In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heatconducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a timedependent domain which ... 
Maximal operators on the infinitedimensional torus
(20220331)We study maximal operators related to bases on the infinitedimensional torus $\tom$. {For the normalized Haar measure $dx$ on $\mathbb{T}^\omega$ it is known that $M^{\mathcal{R}_0}$, the maximal operator associated with ... 
Entire vortex solutions of negative degree for the anisotropic GinzburgLandau system
(2022)The anisotropic GinzburgLandau system $\Delta u+\delta \nabla (div u) +\delta curl^*(curl u)=(u^21) u$, for $u\colon\mathbb R^2\to\mathbb R^2$ and $\delta\in (1,1)$, models the formation of vortices in liquid crystals. ... 
Cubic microlattices embedded in nematic liquid crystals: A Landaude Gennes study
(20210101)We consider a Landaude Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not ... 
On the Hausdorff dimension of Riemann's nondifferentiable function
(20210101)Recent findings show that the classical Riemann's nondifferentiable function has a physical and geometric nature as the irregular trajectory of a polygonal vortex filament driven by the binormal flow. In this article, we ... 
A pseudospectral method for the onedimensional fractional Laplacian on R
(20210115)In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map ... 
Discrepancy of Minimal Riesz Energy Points
(20211201)We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz senergy on the sphere Sd. Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished ... 
Selfadjointness of twodimensional Dirac operators on corner domains
(20210101)We investigate the selfadjointness of the twodimensional Dirac operator D, with quantumdot and Lorentzscalar ishell boundary conditions, on piecewise C2 domains (with finitely many corners). For both models, we prove ... 
Dirac Operators and Shell Interactions: A Survey
(20210101)In this survey we gather recent results on Dirac operators coupled with δshell interactions. We start by discussing recent advances regarding the question of selfadjointness for these operators. Afterwards we switch to ... 
On the regularity of solutions to the kgeneralized kortewegde vries equation
(20180101)This work is concerned with special regularity properties of solutions to the kgeneralized Kortewegde Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ... 
Topics in the mathematical design of materials
(20210101)We present a perspective on several current research directions relevant to the mathematical design of new materials. We discuss: (i) design problems for phasetransforming and shapemorphing materials, (ii) epitaxy as an ... 
The Frisch–Parisi formalism for fluctuations of the Schrödinger equation
(2022)We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, \delta}(t)$ be the fluctuations in time of $\int\lvert x \rvert^{2\delta}\lvert ... 
On the Schrödinger map for regular helical polygons in the hyperbolic space
(20220101)The main purpose of this article is to understand the evolution of X t = X s ∧− X ss , with X(s, 0) a regular polygonal curve with a nonzero torsion in the threedimensional Minkowski space. Unlike in the case of the ... 
The Two Dimensional Liquid Crystal Droplet Problem with Tangential Boundary Condition
(20220118)This paper studies a shape optimization problem which reduces to a nonlocal free boundary problem involving perimeter. It is motivated by a study of liquid crystal droplets with a tangential anchoring boundary condition ...