Now showing items 89-108 of 108

• #### The dynamics of vortex filaments with corners ﻿

(Communications on Pure and Applied Analysis (CPAA), 2015-07-01)
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 so-called binormal flow. The case of a regular polygon ...
• #### The initial value problem for the binormal flow with rough data ﻿

(Annales Scientifiques de l'Ecole Normale Superieure, 2015-12-31)
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 ...
• #### The Vortex Filament Equation as a Pseudorandom Generator ﻿

(Acta Applicandae Mathematicae, 2015-08-01)
In this paper, we consider the evolution of the so-called 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 ...
• #### Three Observations on Commutators of Singular Integral Operators with BMO Functions ﻿

(AWM-Springer Series, Harmonic Analysis, Partial Differentail Equations, Complex Analysis, Banach Spaces, and Operator Theory, 2016-07-01)
• #### Weghted Lorentz and Lorentz-Morrey estimates to viscosity solutions of fully nonlinear elliptic equations ﻿

(Complex Variables and Elliptic Equations, 2018)
We prove a global weighted Lorentz and Lorentz-Morrey estimates of the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equation $F(D^{2}u,x)=f(x)$ defined in a bounded $C^{1,1}$ domain. The ...
• #### Weighted mixed weak-type inequalities for multilinear operators ﻿

(Studia Mathematica, 2017)
In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main ...
• #### Weighted norm inequalities for rough singular integral operators ﻿

(Journal of Geometric Analysis, 2018-08-17)
In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index ...
• #### Zero limit of entropic relaxation time for the Shliomis model of ferrofluids ﻿

(2018-02-11)
We construct solutions for the Shilomis model of ferrofluids in a critical space, uniformly in the entropic relaxation time $\tau \in (0, \tau_0)$. This allows us to study the convergence when $\tau\to 0$ for such solutions.