Now showing items 37-56 of 97

• #### Invariant measures for the dnls equation ﻿

(2020-10-02)
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 $\mathbb{R}^3$ ﻿

(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 ...
• #### Lorentz estimates for asymptotically regular fully nonlinear parabolic equations ﻿

(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 ﻿

(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 domain-twin boundary interactions in Ni-Mn-Ga ﻿

(2020-04)
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 ...
• #### Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions ﻿

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

(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 ﻿

(2017-07-18)
• #### On the unique continuation of solutions to non-local non-linear dispersive equations ﻿

(2020-08-02)
We prove unique continuation properties of solutions to a large class of nonlinear, non-local 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 ﻿

(2020-07-02)
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 ...