Qinfeng Li

activity

20192026

most citedOn Laplacian eigenvalue equation with constant Neumann boundary data

3 citations · 7 across the 15 of their papers we have counts for

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16 papers · 1 filter

math.AP2026

A Quantitative Pólya--Szegő Theorem for Tangential Polygons

Changfeng Gui, Yeyao Hu, Qinfeng Li

For a bounded Lipschitz domain $Ω \subset R^{2}$ , let $T (Ω) = \int_{Ω} u_{Ω} d x$ denote its torsional rigidity, where $- Δ u_{Ω} = 1$ in $Ω$ and $u_{Ω} = 0$ on $\partial Ω$ . We prove a quantit…

math.AP2026

Serrin's Problem under Dirichlet Perturbations: Geometric Compactness and Sharp Planar Stability

Qinfeng Li, Weihong Xie, Hang Yang

In earlier work [21], we posed a stability question for Serrin's overdetermined problem under Dirichlet perturbations and proved that the answer is negative in dimensions $n \geq 3$ .…

math.AP2026

Mixed Torsion on Right Triangles and the Pólya--Szegő Monotonicity Problem for Regular Polygons

Changfeng Gui, Yeyao Hu, Qinfeng Li +1

Motivated by the polygonal Pólya--Szegő conjecture for torsional rigidity, we study two monotonicity problems for torsional rigidity. The first concerns a mixed torsion problem on…

math.AP2026

Global Strict Monotonicity and Asymptotics of the First Steklov Eigenvalue for Regular Polygons

Zhuo Cheng, Changfeng Gui, Yeyao Hu +2

For a bounded Lipschitz planar domain $Ω$ , let $σ_{1} (Ω)$ denote its first nonzero Steklov eigenvalue. Let $Ω_{N}$ be the regular $N$ -gon normalized to have perimeter $2 π$ . We prove th…

math.AP2024

On the location of the maximal gradient of the torsion function over some non-symmetric planar domains

Qinfeng Li, Shuangquan Xie, Hang Yang +1

We investigate the location of the maximal gradient of the torsion function on certain non-symmetric planar domains. First, by establishing uniform estimates for convex narrow doma…

math.AP2023

Torsion energy with boundary mean zero condition

Qinfeng Li, Weihong Xie, Hang Yang

Motivated by establishing Neumann Talenti type comparison results, we concern the minimization of the following shape functional under volume constraint: \begin{align*} T(Ω):=\inf\…

math.AP2023

A stronger constant rank theorem

Qinfeng Li, Lu Xu

Motivated from one-dimensional rigidity results of entire solutions to Liouville equation, we consider the semilinear equation \begin{align} \label{liouvilleequationab} Δu=G(u) \qu…

math.AP2023

On location of maximum of gradient of torsion function

Qinfeng Li, Ruofei yao

It has been a widely belief that for a planar convex domain with two coordinate axes of symmetry, the location of maximal norm of gradient of torsion function is either linked to c…

math.AP2023

Heat Transfer Shape Optimization: Stability and Non-Optimality of the Ball

Qinfeng Li, Hang Yang

This paper investigates shape optimization problems in the context of heat transfer, with a focus on the stability and non-optimality of round domains under Robin boundary conditio…

math.AP2023★ 1 cited

Concentration breaking on two optimization problems

Yong Huang, Qinfeng Li, Qiuqi Li

In the present paper, we study the boundary concentration breaking phenomena on two thermal insulation problems considered on Lipschitz domains, based on Serrin's overdetermined re…

math.AP2022★ 3 cited

On Laplacian eigenvalue equation with constant Neumann boundary data

Yong Huang, Qinfeng Li, Qiuqi Li +1

Let $Ω$ be a bounded Lipshcitz domain in $R^{n}$ and we study boundary behaviors of solutions to the Laplacian eigenvalue equation with constant Neumann data. \begin{align}…

math.AP2022

On smooth interior approximation of Sets of Finite Perimeter

Changfeng Gui, Yeyao Hu, Qinfeng Li

In this paper, we prove that for any bounded set of finite perimeter $Ω \subset R^{n}$ , we can choose smooth sets $E_{k} ⋐ Ω$ such that $E_{k} \to Ω$ in $L^{1}$ and \…

math.AP2022

Some geometric inequalities related to Liouville equation

Changfeng Gui, Qinfeng Li

In this paper, we prove that if $u$ is a solution to the Liouville equation \begin{align} \label{scalliouville} Δu+e^{2u} =0 \quad \mbox{in $R^{2}$ ,} \end{align}then the dia…

math.AP2022★ 3 cited

Rigidity results on Liouville equation

Alexandre Eremenko, Changfeng Gui, Qinfeng Li +1

We give a complete classification of solutions bounded from above of the Liouville equation $$-Δu=e^{2u}\quad\mbox{in}\quad {\mathbf{R}}^2.$$ More generally, solutions in the class…

math.AP2020

Stability analysis on the thermal insulation problems

Yong Huang, Qinfeng Li, Qiuqi Li

Based on the domain variational point of view, we carry on stability analysis on two shape optimization problems from thermal insulation background. The novelty is that, we do not…

math.AP2019

Some Energy Estimates for Stable Solutions to Fractional Allen-Cahn Equations

Changfeng Gui, Qinfeng Li

In this paper we study stable solutions to the fractional equation \begin{align} (-Δ)^s u =f(u), \quad |u| < 1 \quad \mbox{in $R^{d}$ }, \end{align}where $0 < s < 1$ and $f:[-1,1…