Shanlin Huang

activity

20142026

most citedInhomogeneous Oscillatory Integrals and Global Smoothing Effects for Dispersive Equations

15 citations · 32 across the 12 of their papers we have counts for

collaborators

13 papers

math.AP2026

Fractal Turán-Nazarov Inequality and Observability for Schrödinger Equations

Jiaqi Yu, Shanlin Huang

This paper establishes limitations on observability inequality and unique continuation for Schrödinger equations on fractal sets. We prove that, in contrast to the heat equation, s…

math.AP2024

Pointwise estimates for the fundamental solutions of higher order Schrödinger equations in odd dimensions II: high dimensional case

Han Cheng, Shanlin Huang, Tianxiao Huang +1

In this paper, for any odd $n$ and any integer $m \geq 1$ with $n > 4 m$ , we study the fundamental solution of the higher order Schrödinger equation \begin{equation*} \mathrm{i}\partial…

math.CA2023

Heisenberg Uniqueness Pairs and the wave equation

Shanlin Huang, Jiaqi Yu

Given a curve $Γ$ and a set $Λ$ in the plane, the concept of the Heisenberg uniqueness pair $(Γ, Λ)$ was first introduced by Hedenmalm and Motes-Rodr\'ıgez (Ann. of Math. 173(2),15…

math.AP2022

Dispersive estimates for the Schrödinger equation with finite rank perturbations

Han Cheng, Shanlin Huang, Quan Zheng

In this paper, we investigate dispersive estimates for the time evolution of Hamiltonians $$ H=-Δ+\sum_{j=1}^N\langle\cdot\,, φ_j\rangle φ_j\quad\,\,\,\text{in}\,\,\,\mathbb{R}^d,\…

math.AP2020

Characterizations of stabilizable sets for some parabolic equations in $R^{n}$

Shanlin Huang, Gengsheng Wang, Ming Wang

We consider the parabolic type equation in $R^{n}$ : \begin{align}\label{equ-0} (\partial_t+H)y(t,x)=0,\,\,\, (t,x)\in (0,\infty)\times\mathbb{R}^n;\;\; \quad y(0,x)\in L^2(\…

math.OC2020

Observable sets, potentials and Schrödinger equations

Shanlin Huang, Gengsheng Wang, Ming Wang

We characterize observable sets for 1-dim Schrödinger equations in $R$ : $i \partial_{t} u = (- \partial_{x}^{2} + x^{2 m}) u$ (with $m \in N := {0, 1, \dots}$ ). More precisely,…

math.AP2019★ 6 cited

Unique continuation properties for one dimensional higher order Schrödinger equations

Tianxiao Huang, Shanlin Huang, Quan Zheng

We study two types of unique continuation properties for the higher order Schrödinger equation with potential $$ i\partial_tu=(-Δ_x)^mu+V(t,x)u,\quad(t,x)\in\mathbb{R}^{1+n},\,2\le…

math.AP2017★ 4 cited

Uncertainty principle, minimal escape velocities and observability inequalities for schrödinger equations

Shanlin Huang, Avy Soffer

We develop a new abstract derivation of the observability inequalities at two points in time for Schrödinger type equations. Our approach consists of two steps. In the first step w…

math.AP2017★ 15 cited

Inhomogeneous Oscillatory Integrals and Global Smoothing Effects for Dispersive Equations

Tianxiao Huang, Shanlin Huang, Quan Zheng

We study oscillatory integrals of the type $F^{- 1} (e^{i t a (\cdot)} ψ (\cdot))$ where $a$ is a general function satisfying some elliptic type and non-degenerate conditions a…

math.AP2016★ 3 cited

Remarks on $L^{p}$ -limiting absorption principle of Schrödinger operators and applications to spectral multiplier theorems

Shanlin Huang, Xiaohua Yao, Quan Zheng

This paper comprises two parts. We first investigate a $L^{p}$ type of limiting absorption principle for Schrödinger operators $H = - Δ + V$ , i.e., In $R^{n}$ ( $n \geq 3$ ) we prove t…

math.AP2015★ 1 cited

$L^{p}$ estimates for fractional schrodinger operators with kato class potentials

Shanlin Huang, Ming Wang, Quan Zheng +1

Let $α > 0$ , $H = (- △)^{α} + V (x)$ , $V (x)$ belongs to the higher order Kato class $K_{2α}(\mathbbm{R}^n)$. For $1 \leq p \leq \infty$ , we prove a polynomial upper bound of $\|e^{-itH…

math.AP2015

Quantitative uniqueness of some higher order elliptic equations

Shanlin Huang, Ming Wang, Quan Zheng

We study the quantitative unique continuation property of some higher order elliptic operators. In the case of $P = (- Δ)^{m}$ , where $m$ is a positive integer, we derive lower bounds o…

math.AP2014★ 3 cited

Concerning $L^{p}$ resolvent estimates for simply connected manifolds of constant curvature

Shanlin Huang, Christopher D. Sogge

We prove families of uniform $(L^{r}, L^{s})$ resolvent estimates for simply connected manifolds of constant curvature (negative or positive) that imply the earlier ones for Euclidean s…