Now showing items 188-207 of 208

• #### Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane ﻿

(2018-12)
For electric and magnetic potentials with compact support, we consider the magnetic Schrödinger equation with fixed positive energy. Under a mild additional regularity hypothesis, and with fixed magnetic potential, we show ...
• #### Uniqueness and Properties of Distributional Solutions of Nonlocal Equations of Porous Medium Type ﻿

(2016-09-01)
We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem for the anomalous diffusion equation $\partial_tu-\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ ...
• #### Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7 ﻿

(2018-09-01)
For ε>0, we consider the Ginzburg-Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, we prove that for every ε>0, there exists a unique global ...
• #### Uniqueness properties for discrete equations and Carleman estimates ﻿

(2017-03-25)
Using Carleman estimates, we give a lower bound for solutions to the discrete Schrödinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of ...
• #### Uniqueness Properties of Solutions to the Benjamin-Ono equation and related models ﻿

(2019-01-31)
We prove that if u1, u2 are solutions of the Benjamin- Ono equation defined in (x, t) ∈ R × [0, T ] which agree in an open set Ω ⊂ R × [0,T], then u1 ≡ u2. We extend this uniqueness result to a general class of equations ...
• #### Uniqueness properties of solutions to the Benjamin-Ono equation and related models ﻿

(2020-03-15)
We prove that if u1,u2 are real solutions of the Benjamin-Ono equation defined in (x,t)∈R×[0,T] which agree in an open set Ω⊂R×[0,T], then u1≡u2. We extend this uniqueness result to a general class of equations of Benjamin-Ono ...
• #### Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds ﻿

(2018)
The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian ...
• #### Variable Lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities ﻿

(2018-02-15)
We prove global Calder\'on-Zygmund type estimate in Lorentz spaces for variable power of the gradients to weak solution of nonlinear elliptic equations in a non-smooth domain. We mainly assume that the nonlinearities are ...
• #### Variation bounds for spherical averages ﻿

(2021-06-22)
We consider variation operators for the family of spherical means, with special emphasis on $L^p\to L^q$ estimates
• #### Vector-valued extensions for fractional integrals of Laguerre expansions ﻿

(2018)
We prove some vector-valued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted $L^p-L^q$ vector-valued extensions, in a multidimensional ...
• #### Vector-valued operators, optimal weighted estimates and the $C_p$ condition ﻿

(2018-09)
In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ...
• #### Vortex filament equation for a regular polygon ﻿

(2014-12-31)
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 ...
• #### Vortex Filament Equation for a regular polygon in the hyperbolic plane ﻿

(2020-07-09)
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 ﻿

(2020-06-15)
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 ...

(2017-07)
• #### The Well Order Reconstruction Solution for Three-Dimensional Wells, in the Landau-de Gennes theory. ﻿

(2019)
We study nematic equilibria on three-dimensional 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 three-dimensional wells, in the Landau–de Gennes theory ﻿

(2020-03-01)
We study nematic equilibria on three-dimensional 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 ...