arXiv subjects

Shanlin Huang

Publications and source records attributed to Shanlin Huang.

21 records · Page 2Linked to original sources

arXiv2017

Inhomogeneous Oscillatory Integrals and Global Smoothing Effects for Dispersive Equations

We study oscillatory integrals of the type ${\mathcal F}^{-1}(e^{ita(\cdot)}ψ(\cdot))$ where $a$ is a general function satisfying some elliptic type and non-degenerate conditions at both the origin and infinity, and $ψ$ belongs to some symbol class. Point-wise estimates in space-time are gained with partial sharpness. As applications, global smoothing effects of $L^p-L^q$ as well as Strichartz type for dispersive equations are studied. An application to fractional Schrödinger equations is also given.

math.AP↗

arXiv2015

Quantitative uniqueness of some higher order elliptic equations

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 of decay at infinity for any nontrivial solutions under some general assumptions. Furthermore, in dimension 2, we can obtain essentially sharp lower bounds for some forth order elliptic operators, the sharpness is shown by constructing a Meshkov type example.

math.AP↗

arXiv2014

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

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 space of Kenig, Ruiz and the second author \cite{KRS}. In the case of the sphere we take advantage of the fact that the half-wave group of the natural shifted Laplacian is periodic. In the case of hyperbolic space, the key ingredient is a natural variant of the Stein-Tomas restriction theorem.

math.AP↗