Now showing items 47-66 of 119

• #### 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].
• #### Modeling cardiac structural heterogeneity via space-fractional differential equations ﻿

(Computational and Mathematical Biomedical Engineering (CMBE2017) Proceedings, 2017)
We discuss here the use of non-local models in space and fractional order operators in the characterisation of structural complexity and the modeling of propagation in heterogeneous biological tissues. In the specific, we ...
• #### Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications ﻿

(Mathematical Inequalities & Applications, 2017-07-18)
Let $I_{v}\left( x\right)$ be modified Bessel functions of the first kind. We prove the monotonicity property of the function $x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ... • #### New bounds for bilinear Calderón-Zygmund operators and applications ﻿ (Revista Matemática Iberoamericana, 2016-11-25) In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following ... • #### Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications ﻿ (Adv. Math., 2018) The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size$h>0$$(-\Delta_h)^su=f,$ for$u,f:\Z_h\to\R$,$0<s<1$, is performed. The pointwise nonlocal ... • #### A note on the off-diagonal Muckenhoupt-Wheeden conjecture ﻿ (WSPC Proceedings, 2016-07-01) We obtain the off-diagonal Muckenhoupt-Wheeden conjecture for Calderón-Zygmund operators. Namely, given$1 < p < q < \infty$and a pair of weights$(u; v)$, if the Hardy-Littlewood maximal function satisfies the following ... • #### On a hyperbolic system arising in liquid crystal modelling ﻿ (Journal of Hyperbolic Differential Equations, 2017-11) We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution ... • #### On Bloom type estimates for iterated commutators of fractional integrals ﻿ (Indiana University Mathematics Journal, 2018-04) In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. We give new proofs for those inequalities relying upon a new sparse ... • #### On pointwise and weighted estimates for commutators of Calderón-Zygmund operators ﻿ (Advances in Mathematics, 2017) In recent years, it has been well understood that a Calderón-Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar ... • #### On sums involving Fourier coefficients of Maass forms for SL(3,Z) ﻿ (2016-09-10) We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for SL(3,Z), and as an application obtain a pointwise estimate and a second moment estimate for the sums ... • #### 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 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 influence of gravity on density-dependent incompressible periodic fluids ﻿ (J. Differential Equations, 2019) The present work is devoted to the analysis of density-dependent, incompressible fluids in a 3D torus, when the Froude number$\varepsilon$goes to zero. We consider the very general case where the initial data do not have ... • #### 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 ...
• #### Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations ﻿

(Journal of Biological Dynamics, 2016-09-01)
The Lotka-Volterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting ...