Browsing Analysis of Partial Differential Equations (APDE) by Issue Date
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Relativistic Hardy Inequalities in Magnetic Fields
(Journal of Statistical Physics, 20141231)We deal with Dirac operators with external homogeneous magnetic fields. Hardytype inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality ... 
Vortex filament equation for a regular polygon
(Nonlinearity, 20141231)In this paper, we study the evolution of the vortex filament equation,$$ X_t = X_s \wedge X_{ss},$$with $X(s, 0)$ being a regular planar polygon. Using algebraic techniques, supported by full numerical simulations, we give ... 
Spectral asymptotics of the Dirichlet Laplacian in a conical layer
(Communications on Pure and Applied Analysis, 20150501)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 ... 
The dynamics of vortex filaments with corners
(Communications on Pure and Applied Analysis (CPAA), 20150701)This paper focuses on surveying some recent results obtained by the author together with V. Banica on the evolution of a vortex filament with one corner according to the socalled binormal flow. The case of a regular polygon ... 
The Vortex Filament Equation as a Pseudorandom Generator
(Acta Applicandae Mathematicae, 20150801)In this paper, we consider the evolution of the socalled vortex filament equation (VFE), $$ X_t = X_s \wedge X_{ss},$$ taking a planar regular polygon of M sides as initial datum. We study VFE from a completely novel ... 
The initial value problem for the binormal flow with rough data
(Annales Scientifiques de l'Ecole Normale Superieure, 20151231)In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove that under suitable conditions on the ... 
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 ... 
Meanfield dynamics of the spinmagnetization coupling in ferromagnetic materials: Application to currentdriven domain wall motions
(IEEE Transactions on Magnetics, 20151231)In this paper, we present a meanfield model of the spinmagnetization coupling in ferromagnetic materials. The model includes nonisotropic diffusion for spin dynamics, which is crucial in capturing strong spinmagnetization ... 
Shell interactions for Dirac operators: On the point spectrum and the confinement
(SIAM Journal on Mathematical Analysis, 20151231)Spectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H =i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$ and $V$ is a measurevalued potential. The ... 
Erratum to: Relativistic Hardy Inequalities in Magnetic Fields [J Stat Phys, 154, (2014), 866876, DOI 10.1007/s1095501409150]
(Journal of Statistical Physics, 20151231)[No abstract available] 
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 ... 
Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer
(Colloquium Mathematicum, 20160101)In this paper we study mixed weighted weaktype 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]. 
Global Uniqueness for The Calderón Problem with Lipschitz Conductivities
(Forum of Mathematics, Pi, 20160101)We prove uniqueness for the Calderón problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three and fourdimensional cases, this confirms a conjecture of ... 
Inverse scattering for a random potential
(201605)In this paper we consider an inverse problem for the $n$dimensional random Schrödinger equation $(\Deltaq+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a ... 
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 ... 
Quantitative weighted mixed weaktype inequalities for classical operators
(Indiana University Mathematics Journal, 20160630)We improve on several mixed weak type inequalities both for the HardyLittlewood maximal function and for CalderónZygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by ... 
On the bound states of Schrödinger operators with $\delta$interactions on conical surfaces
(Communications in Partial Differential Equations, 20160630)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 ... 
Reverse Hölder Property for Strong Weights and General Measures
(Journal of Geometric Analysis, 20160630)We present dimensionfree reverse Hölder inequalities for strong $A^{\ast}_p$ weights, $1 \le p < \infty$. We also provide a proof for the full range of local integrability of $A^{\ast}_1$ weights. The common ingredient ... 
Three Observations on Commutators of Singular Integral Operators with BMO Functions
(AWMSpringer Series, Harmonic Analysis, Partial Differentail Equations, Complex Analysis, Banach Spaces, and Operator Theory, 20160701)Three observations on commutators of Singular Integral Operators with BMO functions are exposed, namely 1  The already known subgaussian local decay for the commutator, namely $\[\frac{1}{Q}\left\left\{x\in Q\, : ... 
A note on the offdiagonal MuckenhouptWheeden conjecture
(WSPC Proceedings, 20160701)We obtain the offdiagonal MuckenhouptWheeden conjecture for CalderónZygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the HardyLittlewood maximal function satisfies the following ...