• Asymptotic behaviour of neuron population models structured by elapsed-time 

  Cañizo J.A.; Yoldas H. (Nonlinearity, 2019-01-04)

  We study two population models describing the dynamics of interacting neurons, initially proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J. Math. Neurosci. 4 1–26). In the first model, the ...

• El efecto de Talbot: de la óptica a la ecuación de Schrödinger 

  Eceizabarrena D. (TEMat, 2017-07)

  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 ...

• Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments 

  del Teso F.; Endal J.; Jakobsen E.R. (SIAM Journal on Numerical Analysis, 2018)

  \noindent We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t) \qquad\text{in}\qquad ...

• On the regularity of solutions to the k-generalized korteweg-de vries equation 

  Kenig C.E.; Linares F.; Ponce G.; Vega L. (Proceedings of the American Mathematical Society, 2018-07)

  This work is concerned with special regularity properties of solutions to the k-generalized Korteweg-de Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ...

• Absence of eigenvalues of two-dimensional magnetic Schroedinger operators 

  Fanelli L.; Krejcirik D.; Vega L. (2018-01-01)

  By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schroedinger operator possesses no point ...

• Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation 

  Correia S.; Côte R.; Vega L. (2018-07-06)

  We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. ...

• On the improvement of the Hardy inequality due to singular magnetic fields 

  Fanelli L.; Krejcirik D.; Laptev A.; Vega L. (2018-07-12)

  We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ...

• Regularity of fractional maximal functions through Fourier multipliers 

  Beltran D.; Ramos J. P.; Saari O. (2018)

  We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n \geq 2$. We also show that the spherical fractional maximal function ...

• Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds 

  Beltran D.; Hickman J.; Sogge C. D. (2018)

  The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian ...

• Sparse bounds for pseudodifferential operators 

  Beltran D.; Cladek L. (Journal d'Analyse Mathématique, 2018)

  We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of ...

• Spectral stability of Schrödinger operators with subordinated complex potentials 

  Fanelli L.; Krejcirik D.; Vega L. (Journal of Spectral Theory, 2018-06-28)

  We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness condition. By developing ...

• On the Relationship between the One-Corner Problem and the $M-$Corner Problem for the Vortex Filament Equation 

  De la Hoz F.; Vega L. (Journal of Nonlinear Science, 2018-06-28)

  In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular M-corner polygon as initial datum can be explained at infinitesimal times as the superposition of M one-corner initial ...

• Sharp exponential localization for eigenfunctions of the Dirac Operator 

  Cassano B. (2018)

  We determine the fastest possible rate of exponential decay at infinity for eigenfunctions of the Dirac operator $\mathcal D_n + \mathbb V$, being $\mathcal D_n$ the massless Dirac operator in dimensions $n=2,3$ and ...

• Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials 

  Cassano B.; Pizzichillo F. (Letters in Mathematical Physics, 2018)

  We describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, ...

• Variable Lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities 

  Liang S.; Zheng S. (Nonlinear Analysis, 2018-02-15)

  We prove global Calder\'on-Zygmund type estimate in Lorentz spaces for variable power of the gradients to weak solution of nonlinear elliptic equations in a non-smooth domain. We mainly assume that the nonlinearities are ...

• Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients 

  Zheng S.; Tian H. (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 ...

• Weghted Lorentz and Lorentz-Morrey estimates to viscosity solutions of fully nonlinear elliptic equations 

  Junjie Zhang,Shenzhou Zheng (Complex Variables and Elliptic Equations, 2018)

  We prove a global weighted Lorentz and Lorentz-Morrey estimates of the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equation $F(D^{2}u,x)=f(x)$ defined in a bounded $C^{1,1}$ domain. The ...

• Singular Perturbation of the Dirac Hamiltonian 

  Pizzichillo F. (2017-12-15)

  This thesis is devoted to the study of the Dirac Hamiltonian perturbed by delta-type potentials and Coulomb-type potentials. We analysed the delta-shell interaction on bounded and smooth domains and its approximation by ...

• Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$ 

  Mas A; Pizzichillo F. (Analysis & PDE, 2017-11)

  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 re-scaling of $\mathbf{V}$, converges in the strong resolvent sense ...

• Asymptotic behaviour for fractional diffusion-convection equations 

  Ignat L.; Stan D. (2017-10)

  We consider a convection-diffusion model with linear fractional diffusion in the sub-critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective ...

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