Browsing Analysis of Partial Differential Equations (APDE) by Title
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A Meanfield model for spin dynamics in multilayered ferromagnetic media
(Multiscale Modeling and Simulation, 20151231)In this paper, we develop a meanfield model for describing the dynamics of spintransfer torque in multilayered ferromagnetic media. Specifically, we use the techniques of Wigner transform and moment closure to connect the ... 
$A_1$ theory of weights for rough homogeneous singular integrals and commutators
(20160701)Quantitative $A_1A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \T_\Omega ... 
$A_1$ theory of weights for rough homogeneous singular integrals and commutators
(Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V, 2019)Quantitative $A_1A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $\BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \T_\Omega ... 
Absence of eigenvalues of twodimensional magnetic Schroedinger operators
(20180101)By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding twodimensional Schroedinger operator possesses no point ... 
An atomistic/continuum coupling method using enriched bases
(Multiscale Modeling and Simulation, 20151231)A common observation from an atomistic to continuum coupling method is that the error is often generated and concentrated near the interface, where the two models are combined. In this paper, a new method is proposed to ... 
An IsoperimetricType Inequality for Electrostatic Shell Interactions for Dirac Operators
(Communications in Mathematical Physics, 20160601)In this article we investigate spectral properties of the coupling $H + V_{\lambda}$, where $H =i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$, $m>0$ and $V_{\lambda}$ is an electrostatic shell ... 
Asymptotic behaviour for fractional diffusionconvection equations
(201710)We consider a convectiondiffusion model with linear fractional diffusion in the subcritical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective ... 
Asymptotic behaviour of neuron population models structured by elapsedtime
(Nonlinearity, 20190104)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 ... 
Asymptotic models for free boundary flow in porous media
(Physica D, 2019)We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to ... 
Asymptotics in Fourier space of selfsimilar solutions to the modified Kortewegde Vries equation
(20180706)We give the asymptotics of the Fourier transform of selfsimilar solutions to the modified Kortewegde Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. ... 
Bilinear identities involving the $k$plane transform and Fourier extension operators
(2019)We prove certain $L^2(\mathbb{R}^n)$ bilinear estimates for Fourier extension operators associated to spheres and hyperboloids under the action of the $k$plane transform. As the estimates are $L^2$based, they follow from ... 
Bilinear representation theorem
(Transactions of the American Mathematical Society, 20180101)We represent a general bilinear CalderónZygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so ... 
Bloom type inequality for biparameter singular integrals: efficient proof and iterated commutators
(International Mathematics Research Notices, 20190314)Utilising some recent ideas from our bilinear biparameter theory, we give an efficient proof of a twoweight Bloom type inequality for iterated commutators of linear biparameter singular integrals. We prove that if $T$ ... 
Bloom type upper bounds in the product BMO setting
(Journal of Geometric Analysis, 20190408)We prove some Bloom type estimates in the product BMO setting. More specifically, for a bounded singular integral $T_n$ in $\mathbb R^n$ and a bounded singular integral $T_m$ in $\mathbb R^m$ we prove that $$ \ [T_n^1, ... 
Borderline Weighted Estimates for Commutators of Singular Integrals
(Israel Journal of Mathematics, 20160701)In this paper we establish the following estimate \[ w\left(\left\{ x\in\mathbb{R}^{n}\,:\,\left[b,T]f(x)\right > \lambda\right\} \right)\leq \frac{c_{T}}{\varepsilon^{2}}\int_{\mathbb{R}^{n}}\Phi\left(\b\_{BMO}\f ... 
Boundary Triples for the Dirac Operator with CoulombType Spherically Symmetric Perturbations
(Journal of Mathematical Physics, 201902)We determine explicitly a boundary triple for the Dirac operator $H:=i\alpha\cdot \nabla + m\beta + \mathbb V(x)$ in $\mathbb R^3$, for $m\in\mathbb R$ and $\mathbb V(x)= x^{1} ( \nu \mathbb{I}_4 +\mu \beta i \lambda ... 
The Calderón problem with corrupted data
(Inverse Problems, 201701)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 DirichlettoNeumann map and, therefore, ... 
A characterization of two weight norm inequality for LittlewoodPaley $g_{\lambda}^{*}$function
(Journal of Geometric Analysis, 2017)Let $n\ge 2$ and $g_{\lambda}^{*}$ be the wellknown high dimensional LittlewoodPaley function which was defined and studied by E. M. Stein, $$g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+xy ... 
Convex Integration Arising in the Modelling of ShapeMemory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations
(Journal of Nonlinear Science, 20190330)We study convex integration solutions in the context of the modelling of shapememory alloys. The purpose of the article is twofold, treating both rigidity and flexibility prop erties: Firstly, we relate the maximal ... 
Correlation imaging in inverse scattering is tomography on probability distributions
(Inverse Problems, 20181204)Scattering from a nonsmooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments ...