Browsing Analysis of Partial Differential Equations (APDE) by Title
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On sums involving Fourier coefficients of Maass forms for SL(3,Z)
(20160910)We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for SL(3,Z), and as an application obtain a pointwise estimate and a second moment estimate for the sums ... 
On the absolute divergence of Fourier series in the infinite dimensional torus
(Colloquium Mathematicum, 20190322)In this note we present some simple counterexamples, based on quadratic forms in infinitely many variables, showing that the implication $f\in C^{(\infty}(\mathbb{T}^\omega)\Longrightarrow\sum_{\bar{p}\in\mathbb{Z}^\inf ... 
On the bound states of Schrödinger operators with $\delta$interactions on conical surfaces
(Communications in Partial Differential Equations, 20160630)In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ... 
On the controllability of Partial Differential Equations involving nonlocal terms and singular potentials
(20161212)In this thesis, we investigate controllability and observability properties of Partial Differential Equations describing various phenomena appearing in several fields of the applied sciences such as elasticity theory, ... 
On the energy of critical solutions of the binormal flow
(20190720)The binormal flow is a model for the dynamics of a vortex filament in a 3D inviscid incompressible fluid. The flow is also related with the classical continuous Heisen berg model in ferromagnetism, and the 1D cubic Schr ... 
On the Evolution of the Vortex Filament Equation for regular Mpolygons with nonzero torsion
(20190903)In this paper, we consider the evolution of the Vortex Filament equa tion (VFE): Xt = Xs ∧ Xss, taking Msided regular polygons with nonzero torsion as initial data. Us ing algebraic techniques, backed by numerical ... 
On the global wellposedness of a class of 2D solutions for the Rosensweig system of ferrofluids
(Journal of Differential Equations, 201809)We study a class of 2D solutions of a BlochTorrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are ... 
On the improvement of the Hardy inequality due to singular magnetic fields
(20180712)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the AharonovBohm field in all dimensions and establish a sharp Hardytype ... 
On the improvement of the Hardy inequality due to singular magnetic fields
(20180712)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the AharonovBohm field in all dimensions and establish a sharp Hardytype ... 
On the influence of gravity on densitydependent incompressible periodic fluids
(J. Differential Equations, 2019)The present work is devoted to the analysis of densitydependent, incompressible fluids in a 3D torus, when the Froude number $\varepsilon$ goes to zero. We consider the very general case where the initial data do not have ... 
On the regularity of solutions to the kgeneralized kortewegde vries equation
(Proceedings of the American Mathematical Society, 201807)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 ... 
On the Relationship between the OneCorner Problem and the $M$Corner Problem for the Vortex Filament Equation
(Journal of Nonlinear Science, 20180628)In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular Mcorner polygon as initial datum can be explained at infinitesimal times as the superposition of M onecorner initial ... 
On the smallness condition in linear inviscid damping: monotonicity and resonance chains
(Nonlinearity, 2020)We consider the effects of mixing by smooth bilipschitz shear flows in the linearized Euler equations on $\mathbb{T}_{L}\times\mathbb{R}$. Here, we construct a model which is closely related to a small high frequency ... 
Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations
(Journal of Biological Dynamics, 20160901)The LotkaVolterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting ... 
An optimal scaling to computationally tractable dimensionless models: Study of latex particles morphology formation
(Computer Physics Communications, 202002)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 ... 
Order Reconstruction for neatics on squares with isotropic inclusions: A Landaude Gennes study
(SIAM Journal on Applied Mathematics, 20190330)e study a modified Landaude 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 threedimensional ... 
Partial regularity and smooth topologypreserving approximations of rough domains
(Calculus of Variations and Partial Differential Equations, 20170101)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 weaktype estimates
(Mathematische Annalen, 201809)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\, ... 
Pseudospectral Methods for the Fractional Laplacian on R
(20200702)In this thesis, first, we propose a novel pseudospectral method to approximate accu rately and efficiently the fractional Laplacian without using truncation. More pre cisely, given a bounded regular function defined over ... 
A quantitative approach to weighted Carleson condition
(Concrete Operators, 20170505)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 ...