Browsing Analysis of Partial Differential Equations (APDE) by Title
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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 ... 
An efficient multigrid strategy for largescale molecular mechanics optimization
(20170801)Static mechanical properties of materials require largescale nonlinear optimization of the molecular mechanics model under various controls. This paper presents an efficient multigrid strategy to solve such problems. This ... 
El efecto de Talbot: de la óptica a la ecuación de Schrödinger
(201707)El objetivo de este artículo es dar a conocer un bello efecto óptico que se denomina efecto de Talbot. Primero, describiremos el fenómeno y comentaremos su descubrimiento a mediados del siglo XIX. A continuación, analizaremos ... 
Endpoint estimates, extrapolation for multilinear muckenhoupt classes, and applications
(2019)In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the socalled multilinear Muckenhoupt classes. ... 
Endpoint Sobolev continuity of the fractional maximal function in higher dimensions
(2019)We establish continuity mapping properties of the noncentered fractional maximal operator $M_{\beta}$ in the endpoint input space $W^{1,1}(\mathbb{R}^d)$ for $d \geq 2$ in the cases for which its boundedness is known. ... 
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, ... 
Entire Minimizers of Allen–Cahn Systems with SubQuadratic Potentials
(20210101)We study entire minimizers of the Allen–Cahn systems. The specific feature of our systems are potentials having a finite number of global minima, with subquadratic behaviour locally near their minima. The corresponding ... 
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. ... 
Erratum to: Relativistic Hardy Inequalities in Magnetic Fields [J Stat Phys, 154, (2014), 866876, DOI 10.1007/s1095501409150]
(20151231)[No abstract available] 
Evolution of Polygonal Lines by the Binormal Flow
(20200205)The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr ̈odinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. ... 
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 ... 
Exact Constructions in the (Nonlinear) Planar Theory of Elasticity: From Elastic Crystals to Nematic Elastomers
(202007)In this article we deduce necessary and sufficient conditions for the presence of “Contitype”, highly symmetric, exactly stressfree constructions in the geometrically nonlinear, planar nwell problem, generalising results ... 
The excluded volume of twodimensional convex bodies: shape reconstruction and nonuniqueness
(20190205)In the Onsager model of onecomponent hardparticle systems, the entire phase behaviour is dictated by a function of relative orientation, which represents the amount of space excluded to one particle by another at this ... 
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 ... 
Existence of weak solutions for a general porous medium equation with nonlocal pressure
(201710)We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m1}\nabla (\Delta)^{s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters ... 
Extensions of the JohnNirenberg theorem and applications
(2021)The John–Nirenberg theorem states that functions of bounded mean oscillation are exponentially integrable. In this article we give two extensions of this theorem. The first one relates the dyadic maximal function to the ... 
Flow with $A_\infty(\mathbb R)$ density and transport equation in $\mathrm{BMO}(\mathbb R)$
(201911)We show that, if $b\in L^1(0,T;L^1_{\rm {loc}}(\mathbb R))$ has spatial derivative in the JohnNirenberg space ${\rm{BMO}}(\mathbb R)$, then it generates a unique flow $\phi(t,\cdot)$ which has an $A_\infty(\mathbb R)$ ... 
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 ... 
Gaussian Decay of Harmonic Oscillators and related models
(20170515)We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can ... 
Generalized PoincaréSobolev inequalities
(202012)PoincaréSobolev inequalities are very powerful tools in mathematical analysis which have been extensively used for the study of differential equations and their validity is intimately related with the geometry of the ...