Now showing items 41-60 of 217

• #### A characterization of two weight norm inequality for Littlewood-Paley $g_{\lambda}^{*}$-function ﻿

(2017)
Let $n\ge 2$ and $g_{\lambda}^{*}$ be the well-known high dimensional Littlewood-Paley function which was defined and studied by E. M. Stein, g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+|x-y ...
• #### Spectral asymptotics for $\delta$-interactions on sharp cones ﻿

(2017)
We investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ...
• #### Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients ﻿

(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 ...
• #### The Calderón problem with corrupted data ﻿

(2017-01)
We consider the inverse Calderón problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, ...
• #### Partial regularity and smooth topology-preserving approximations of rough domains ﻿

(2017-01-01)
For a bounded domain $\Omega\subset\mathbb{R}^m, m\geq 2,$ of class $C^0$, the properties are studied of fields of `good directions', that is the directions with respect to which $\partial\Omega$ can be locally represented ...
• #### Singularity formation for the 1-D cubic NLS and the Schrödinger map on $\mathbb{S}^2$ ﻿

(2017-02-02)
In this note we consider the 1-D cubic Schrödinger equation with data given as small perturbations of a Dirac-$\delta$ function and some other related equations. We first recall that although the problem for this type of ...
• #### Quantitative weighted estimates for rough homogeneous singular integrals ﻿

(2017-03-11)
We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space $L^2(w)$, we obtain a bound ...
• #### Uniqueness properties for discrete equations and Carleman estimates ﻿

(2017-03-25)
Using Carleman estimates, we give a lower bound for solutions to the discrete Schrödinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of ...
• #### Sparse domination theorem for multilinear singular integral operators with $L^{r}$-Hörmander condition ﻿

(2017-04-01)
In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the so-called multilinear $L^{r}$-Hörmander condition, then $T$ can be dominated by multilinear sparse operators.
• #### Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions ﻿

(2017-04-28)
In this work, we propose novel discretisations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heat-semigroup formalism. Specifically, we combine suitable ...
• #### A quantitative approach to weighted Carleson condition ﻿

(2017-05-05)
Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator $\mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0$ are ...
• #### Gaussian Decay of Harmonic Oscillators and related models ﻿

(2017-05-15)
We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0-order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can ...
• #### Some remarks on the $L^p$ regularity of second derivatives of solutions to non-divergence elliptic equations and the Dini condition ﻿

(2017-05-30)
In this note we prove an end-point regularity result on the $L^P$ integrability of the second derivatives of solutions to non-divergence form uniformly elliptic equations whose second derivatives are a priori only known ...
• #### Hartree-Fock theory with a self-generated magnetic field ﻿

(2017-06-01)
We prove the existence of a ground state within the Hartree-Fock theory for atoms and molecules, in the presence of self-generated magnetic fields, with and without direct spin coupling. The ground state exists provided ...
• #### Lorentz estimates for asymptotically regular fully nonlinear parabolic equations ﻿

(2017-06-20)
We prove a global Lorentz estimate of the Hessian of strong solutions to the Cauchy-Dirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ ...
• #### Sharp bounds for the ratio of modified Bessel functions ﻿

(2017-06-21)
• #### El efecto de Talbot: de la óptica a la ecuación de Schrödinger ﻿

(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 ...