4 papers · 1 filter
Measure upper bounds of nodal sets of solutions to Dirichlet problem of Schrödinger equations
Hairong Liu, Long Tian, Xiaoping Yang
In this paper, we focus on estimating measure upper bounds of nodal sets of solutions to the following boundary value problem \begin{equation*} \left\{ \begin{array}{lll} Δu+Vu=0\q…
On the number and geometric location of critical points of solutions to a semilinear elliptic equation in annular domains
Haiyun Deng, Hairong Liu, Xiaoping Yang
In this paper, one of our aims is to investigate the instability of the distribution of the critical point set of a solution to a semilinear equation with Diri…
Strong unique continuation property for fourth order Baouendi-Grushin type subelliptic operators with strongly singular potential
Hairong Liu, Xiaoping Yang
In this paper, we prove the strong unique continuation property for the following fourth order degenerate elliptic equation \begin{equation*} Δ^2_{X}u=Vu, \end{equation*} where $Δ_…
Quantitative unique continuation property for solutions to a bi-Laplacian equation with a potential
Hairong Liu, Long Tian, Xiaoping Yang
In this paper, we focus on the quantitative unique continuation property of solutions to \begin{equation*} Δ^2u=Vu, \end{equation*} where . We show that the maxi…