Browsing Analysis of Partial Differential Equations (APDE) by Title
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An efficient multigrid strategy for largescale molecular mechanics optimization
(Journal of Computational Physics, 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
(TEMat, 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 ... 
Erratum to: Relativistic Hardy Inequalities in Magnetic Fields [J Stat Phys, 154, (2014), 866876, DOI 10.1007/s1095501409150]
(Journal of Statistical Physics, 20151231)[No abstract available] 
Existence of weak solutions for a general porous medium equation with nonlocal pressure
(submitted, 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 ... 
Gaussian Decay of Harmonic Oscillators and related models
(Journal of Mathematical Analysis and Applications, 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 ... 
Global Uniqueness for The Calderón Problem with Lipschitz Conductivities
(Forum of Mathematics, Pi, 20160101)We prove uniqueness for the Calderón problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three and fourdimensional cases, this confirms a conjecture of ... 
Global wellposedness and twistwave solutions for the inertial QianSheng model of liquid crystals
(Journal of Differential Equations, 20171002)We consider the inertial QianSheng model of liquid crystals which couples a hyperbolictype equation involving a secondorder material derivative with a forced incompressible NavierStokes system. We study the energy law ... 
A Global wellposedness result for the Rosensweig system of ferrofluids
(Rev. Mat. Iberoam., 2019)In this Paper we study a BlochTorrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of LerayHopf solutions of this ... 
Hardy uncertainty principle, convexity and parabolic evolutions
(Communications in Mathematical Physics, 20160901)We give a new proof of the $L^2$ version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new logconvexity properties and the derivation of ... 
Hardytype inequalities for fractional powers of the DunklHermite operator
(Proc. Edinburgh Math. Soc. (2), 2018)We prove Hardytype inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use hharmonic expansions to reduce the ... 
HartreeFock theory with a selfgenerated magnetic field
(Journal of Mathematical Physics, 20170601)We prove the existence of a ground state within the HartreeFock theory for atoms and molecules, in the presence of selfgenerated magnetic fields, with and without direct spin coupling. The ground state exists provided ... 
Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity
(Revista Matemática Iberoamericana, 201707)We prove that the threedimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero ... 
HölderLebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian
(Discrete Contin. Dyn. Syst., 2018)We study the equations $ \partial_t u(t,n) = L u(t,n) + f(u(t,n),n); \partial_t u(t,n) = iL u(t,n) + f(u(t,n),n)$ and $ \partial_{tt} u(t,n) =Lu(t,n) + f(u(t,n),n)$, where $n\in \mathbb{Z}$, $t\in (0,\infty)$, and $L$ ... 
Improved A1 − A∞ and related estimates for commutators of rough singular integrals
(Proceedings of the Edinburgh Mathematical Society, 2017)An $A_1A_\infty$ estimate improving a previous result in [22] for $[b, T_\Omega]$ with $\Omega\in L^\infty(S^{n1})$ and $b\in BMO$ is obtained. Also a new result in terms of the $A_\infty$ constant and the one ... 
Inverse scattering for a random potential
(201605)In this paper we consider an inverse problem for the $n$dimensional random Schrödinger equation $(\Deltaq+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a ... 
Klein's Paradox and the Relativistic $\delta$shell Interaction in $\mathbb{R}^3$
(Analysis & PDE, 201711)Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable rescaling of $\mathbf{V}$, converges in the strong resolvent sense ... 
Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the oneconstant approximation
(Mathematical Models and Methods in Applied Sciences, 20161231)We consider the twodimensional Landaude Gennes energy with several elastic constants, subject to general $k$radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent ... 
Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
(Mathematische Nachrichten, 20170620)We prove a global Lorentz estimate of the Hessian of strong solutions to the CauchyDirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ ... 
Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients
(Boundary Value Problems, 2017)We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the ... 
Meanfield dynamics of the spinmagnetization coupling in ferromagnetic materials: Application to currentdriven domain wall motions
(IEEE Transactions on Magnetics, 20151231)In this paper, we present a meanfield model of the spinmagnetization coupling in ferromagnetic materials. The model includes nonisotropic diffusion for spin dynamics, which is crucial in capturing strong spinmagnetization ...