Browsing Linear and NonLinear Waves by Title
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Invariant measures for the dnls equation
(20201002)We describe invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schr\"odinger equation (DNLS) constructed in \cite{MR3518561, Genovese2018}. The construction works for small $L^2$ ... 
Klein's Paradox and the Relativistic $\delta$shell Interaction in $\mathbb{R}^3$
(201711)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 rescaling of $\mathbf{V}$, converges in the strong resolvent sense ... 
Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
(20170620)We prove a global Lorentz estimate of the Hessian of strong solutions to the CauchyDirichlet 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
(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 ... 
Magnetic domaintwin boundary interactions in NiMnGa
(202004)The stress required for the propagation of twin boundaries in a sample with fine twins increases monotonically with ongoing deformation. In contrast, for samples with a single twin boundary, the stress exhibits a plateau ... 
Meanfield dynamics of the spinmagnetization coupling in ferromagnetic materials: Application to currentdriven domain wall motions
(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 ... 
Modeling cardiac structural heterogeneity via spacefractional differential equations
(2017)We discuss here the use of nonlocal 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
(20170718)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) ... 
On the bound states of Schrödinger operators with $\delta$interactions on conical surfaces
(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 ... 
On the energy of critical solutions of the binormal flow
(20190720)The binormal flow is a model for the dynamics of a vortex filament in a 3D inviscid incompressible fluid. The flow is also related with the classical continuous Heisen berg model in ferromagnetism, and the 1D cubic Schr ... 
On the energy of critical solutions of the binormal flow
(20200702)The binormal flow is a model for the dynamics of a vortex filament in a 3D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model in ferromagnetism, and the 1D cubic ... 
On the Evolution of the Vortex Filament Equation for regular Mpolygons with nonzero torsion
(20190903)In this paper, we consider the evolution of the Vortex Filament equa tion (VFE): Xt = Xs ∧ Xss, taking Msided regular polygons with nonzero torsion as initial data. Us ing algebraic techniques, backed by numerical ... 
On the improvement of the Hardy inequality due to singular magnetic fields
(20180712)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the AharonovBohm field in all dimensions and establish a sharp Hardytype ... 
On the improvement of the Hardy inequality due to singular magnetic fields
(20180712)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the AharonovBohm field in all dimensions and establish a sharp Hardytype ... 
On the improvement of the Hardy inequality due to singular magnetic fields
(20200901)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the AharonovBohm field in all dimensions and establish a sharp Hardytype ... 
On the regularity of solutions to the kgeneralized kortewegde vries equation
(201807)This work is concerned with special regularity properties of solutions to the kgeneralized Kortewegde Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ... 
On the Relationship between the OneCorner Problem and the $M$Corner Problem for the Vortex Filament Equation
(20180628)In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular Mcorner polygon as initial datum can be explained at infinitesimal times as the superposition of M onecorner initial ... 
On the smallness condition in linear inviscid damping: monotonicity and resonance chains
(2020)We consider the effects of mixing by smooth bilipschitz shear flows in the linearized Euler equations on $\mathbb{T}_{L}\times\mathbb{R}$. Here, we construct a model which is closely related to a small high frequency ... 
On the unique continuation of solutions to nonlocal nonlinear dispersive equations
(20200802)We prove unique continuation properties of solutions to a large class of nonlinear, nonlocal dispersive equations. The goal is to show that if (Formula presented.) are two suitable solutions of the equation defined in ... 
Pseudospectral Methods for the Fractional Laplacian on R
(20200702)In this thesis, first, we propose a novel pseudospectral method to approximate accu rately and efficiently the fractional Laplacian without using truncation. More pre cisely, given a bounded regular function defined over ...