8 papers · 1 filter
Near-boundary rigidity and strict maximum modulus for Neumann eigenfunctions on convex planar domains
Haiyun Deng, Xuyong Jiang, Xiaoping Yang
We prove that the maximum modulus of every nonzero second Neumann eigenfunction on a bounded convex planar domain is attained only on the boundary, without boundary smoothness…
Quantitative characterization of deviations from the hot spots conjecture on convex domains in two-dimensional space forms
Haiyun Deng, Xuyong Jiang, Xiaoping Yang
In this paper, we study critical points of second Neumann eigenfunctions on convex domains in two-dimensional space forms from three complementary perspectives: spectral and geomet…
Symmetry and critical points of second Neumann eigenfunctions on isosceles trapezoids and kites
Haiyun Deng, Changfeng Gui, Xuyong Jiang +3
We classify the symmetry and multiplicity of the second Neumann eigenvalue on isosceles trapezoids and kites as the height varies. Precisely, away from a unique transition height,…
The Sharp Measure Upper Bound of the Nodal Sets of Neumann Laplace Eigenfunctions on C1,1 Domains
Xiujin Chen, Xiaoping Yang
Let Ω be a bounded domain in R^n with C^{1,1} boundary and let u_λ be a Neumann Laplace eigenfunction in Ω with eigenvalue λ. We show that the (n - 1)-dimensional Hausdorff measure…
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…