Browsing Analysis of Partial Differential Equations (APDE) by Title
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Vortex Filament Equation for a regular polygon in the hyperbolic plane
(20200709)The aim of this article is twofold. First, we show the evolution of the vortex filament equation (VFE) for a regular planar polygon in the hyperbolic space. Unlike in the Euclidean space, the planar polygon is open and ... 
Vortex Filament Equation for some Regular Polygonal Curves
(20200615)One of the most interesting phenomena in fluid literature is the occurrence and evolution of vortex filaments. Some of their examples in the real world are smoke rings, whirlpools, and tornadoes. For an ideal fluid, there ... 
Weak and strong $A_p$$A_\infty$ estimates for square functions and related operators
(201707)We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p} ... 
Weak sequential stability for a nonlinear model of nematic electrolytes
(20210101)In this article we study a system of nonlinear PDEs modelling the electrokinetics of a nematic electrolyte material consisting of various ions species contained in a nematic liquid crystal. The evolution is described by a ... 
Weghted Lorentz and LorentzMorrey estimates to viscosity solutions of fully nonlinear elliptic equations
(2018)We prove a global weighted Lorentz and LorentzMorrey 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 weaktype inequalities for multilinear operators
(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
(20180817)In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n1})$ and the BochnerRiesz multiplier at the critical index ... 
The Well Order Reconstruction Solution for ThreeDimensional Wells, in the Landaude Gennes theory.
(2019)We study nematic equilibria on threedimensional square wells, with emphasis on Well Order Reconstruction Solu tions (WORS) as a function of the well size, characterized by λ, and the well height denoted by ε. The WORS ... 
The Well Order Reconstruction Solution for threedimensional wells, in the Landau–de Gennes theory
(20200301)We study nematic equilibria on threedimensional square wells, with emphasis on Well Order Reconstruction Solutions (WORS) as a function of the well size, characterized by 𝜆, and the well height denoted by 𝜖. The WORS ... 
Zero limit of entropic relaxation time for the Shliomis model of ferrofluids
(20180211)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.