Now showing items 34-53 of 104

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

(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 ...
• #### Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the one-constant approximation ﻿

(Mathematical Models and Methods in Applied Sciences, 2016-12-31)
We consider the two-dimensional Landau-de 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, 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 $C^{1,1}$ ...
• #### 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 ...
• #### Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions ﻿

(IEEE Transactions on Magnetics, 2015-12-31)
In this paper, we present a mean-field model of the spin-magnetization coupling in ferromagnetic materials. The model includes non-isotropic diffusion for spin dynamics, which is crucial in capturing strong spin-magnetization ...
• #### Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions ﻿

(Transactions of the American Mathematical Society, 2017)
Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the Dunkl--Hermite operator ...
• #### Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer ﻿

(Colloquium Mathematicum, 2016-01-01)
In this paper we study mixed weighted weak-type inequal- ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2].
• #### Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications ﻿

(Mathematical Inequalities & Applications, 2017-07-18)
• #### On the controllability of Partial Differential Equations involving non-local terms and singular potentials ﻿

(2016-12-12)
In this thesis, we investigate controllability and observability properties of Partial Differential Equations describing various phenomena appearing in several fields of the applied sciences such as elasticity theory, ...
• #### On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids ﻿

(Journal of Differential Equations, 2018-09)
We study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are ...
• #### 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 ...