Analysis of Partial Differential Equations (APDE)
Browse by
Recent Submissions

Vortex Filament Equation for a regular polygon in the hyperbolic plane
(20200709)The aim of this article is twofold. First, we show the evolution of the vortex filament equation (VFE) for a regular planar polygon in the hyperbolic space. Unlike in the Euclidean space, the planar polygon is open and ... 
Riemann's nondifferentiable function and the binormal curvature flow
(20200714)We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object ... 
A Hardytype inequality and some spectral characterizations for the Dirac–Coulomb operator
(20200101)We prove a sharp Hardytype inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrixvalued potentials V of Coulomb type: we characterise ... 
Uniqueness properties of solutions to the BenjaminOno equation and related models
(20200315)We prove that if u1,u2 are real solutions of the BenjaminOno equation defined in (x,t)∈R×[0,T] which agree in an open set Ω⊂R×[0,T], then u1≡u2. We extend this uniqueness result to a general class of equations of BenjaminOno ... 
Asymptotics in Fourier space of selfsimilar solutions to the modified Kortewegde Vries equation
(20200501)We give the asymptotics of the Fourier transform of selfsimilar solutions for the modified Kortewegde Vries equation. In the defocussing case, the selfsimilar profiles are solutions to the Painlevé II equation; although ... 
Evolution of Polygonal Lines by the Binormal Flow
(20200601)The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schrödinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. Finally ... 
On the energy of critical solutions of the binormal flow
(20200702)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 Heisenberg model in ferromagnetism, and the 1D cubic ... 
On the unique continuation of solutions to nonlocal nonlinear dispersive equations
(20200802)We prove unique continuation properties of solutions to a large class of nonlinear, nonlocal dispersive equations. The goal is to show that if (Formula presented.) are two suitable solutions of the equation defined in ... 
On the improvement of the Hardy inequality due to singular magnetic fields
(20200901)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 ... 
A note on generalized FujiiWilson conditions and BMO spaces
(20200701)In this note we generalize the definition of the FujiiWilson condition providing quantitative characterizations of some interesting classes of weights, such as A∞, A∞weak and Cp, in terms of BMO type spaces suited to them. ... 
A note on generalized FujiiWilson conditions and BMO spaces
(20200701)In this note we generalize the definition of the FujiiWilson condition providing quantitative characterizations of some interesting classes of weights, such as A∞, A∞weak and Cp, in terms of BMO type spaces suited to them. ... 
Degenerate PoincareSobolev inequalities
(2021)Abstract. We study weighted Poincar ́e and Poincar ́eSobolev type in equalities with an explicit analysis on the dependence on the Ap con stants of the involved weights. We obtain inequalities of the form with different ... 
Regularity of maximal functions on Hardy–Sobolev spaces
(20181201)We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy–Sobolev spaces H1,p(Rd) when p > d/(d + 1). This range of exponents is sharp. As a byproduct of the ... 
Nondegeneracy of heteroclinic orbits for a class of potentials on the plane
(2021)In the scalar case, the nondegeneracy of heteroclinic orbits is a wellknown property, commonly used in problems involving nonlinear elliptic, parabolic or hyperbolic P.D.E. On the other hand, Schatzman proved that in the ... 
Bilinear Spherical Maximal Functions of Product Type
(20210812)In this paper we introduce and study a bilinear spherical maximal function of product type in the spirit of bilinear Calderón–Zygmund theory. This operator is different from the bilinear spherical maximal function considered ... 
Variation bounds for spherical averages
(20210622)We consider variation operators for the family of spherical means, with special emphasis on $L^p\to L^q$ estimates 
On a probabilistic model for martensitic avalanches incorporating mechanical compatibility
(20210701)Building on the work by Ball et al (2015 MATEC Web of Conf. 33 02008), Cesana and Hambly (2018 A probabilistic model for interfaces in a martensitic phase transition arXiv:1810.04380), Torrents et al (2017 Phys. Rev. E 95 ... 
Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol
(20210824)We study the problem of pointwise convergence for equations of the type $i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and nonsingular. We prove that for initial data $f\in H^s(\mathbb{R}^n)$ ... 
A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores
(2021)We establish a comparison principle providing accurate upper bounds for the modulus of vector valued minimizers of an energy functional, associated when the potential is smooth, to elliptic gradient systems. Our assumptions ... 
Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics
(20210730)In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevreytype spaces as time tends to infinity. Thus, echo chains are shown to ...