Now showing items 21-40 of 52

• #### On the bound states of Schrödinger operators with $\delta$-interactions on conical surfaces ﻿

(Communications in Partial Differential Equations, 2016-06-30)
In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$-interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ...
• #### On the improvement of the Hardy inequality due to singular magnetic fields ﻿

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

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

(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 ...
• #### Reconstruction from boundary measurements for less regular conductivities ﻿

(2016-10-01)
In this paper, following Nachman's idea [14] and Haberman and Tataru's idea [9], we reconstruct $C^1$ conductivity $\gamma$ or Lipchitz conductivity $\gamma$ with small enough value of $|\nabla log\gamma|$ in a Lipschitz ...
• #### Regularity of fractional maximal functions through Fourier multipliers ﻿

(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 ...
• #### Relativistic Hardy Inequalities in Magnetic Fields ﻿

(Journal of Statistical Physics, 2014-12-31)
We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality ...
• #### The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation ﻿

(Journal of Mathematical Physics, 2017-08-03)
This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by ...
• #### Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments ﻿

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

(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 $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, ...
• #### Sharp bounds for the ratio of modified Bessel functions ﻿

(Mediterranean Journal of Mathematics, 2017-06-21)
• #### Spectral asymptotics of the Dirichlet Laplacian in a conical layer ﻿

(Communications on Pure and Applied Analysis, 2015-05-01)
The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture limit. On the one hand, we prove that, for ...
• #### Spectral stability of Schrödinger operators with subordinated complex potentials ﻿

(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 ...