Browsing Analysis of Partial Differential Equations (APDE) by Title
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New bounds for bilinear CalderónZygmund operators and applications
(Revista Matemática Iberoamericana, 20161125)In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following ... 
Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications
(Adv. Math., 2018)The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ \[ (\Delta_h)^su=f, \] for $u,f:\Z_h\to\R$, $0<s<1$, is performed. The pointwise nonlocal ... 
A note on generalized Poincarétype inequalities with applications to weighted improved Poincarétype inequalities
(2020)The main result of this paper supports a conjecture by C. P\'erez and E. Rela about the properties of the weight appearing in their recent selfimproving result of generalized inequalities of Poincar\'etype in the Euclidean ... 
A note on the offdiagonal MuckenhouptWheeden conjecture
(WSPC Proceedings, 20160701)We obtain the offdiagonal MuckenhouptWheeden conjecture for CalderónZygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the HardyLittlewood maximal function satisfies the following ... 
On a hyperbolic system arising in liquid crystal modelling
(Journal of Hyperbolic Differential Equations, 201711)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 ... 
On Bloom type estimates for iterated commutators of fractional integrals
(Indiana University Mathematics Journal, 201804)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 ... 
On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians
(Communications on pure and applied analysis, 201909)We obtain generalised trace Hardy inequalities for fractional powers of general operators given by sums of squares of vector fields. Such inequalities are derived by means of particular solutions of an extended equation ... 
On pointwise and weighted estimates for commutators of CalderónZygmund operators
(Advances in Mathematics, 2017)In recent years, it has been well understood that a CalderónZygmund 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 ... 
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 ...