8 papers · 1 filter
Optimal Rigidity Results for the -Hessian Equation of Lane--Emden Type
Wei Dai, Jingze Fu, Changfeng Gui +1
In this paper, we establish optimal Liouville theorems and classification results for the \(k\)-Hessian Lane--Emden equation \[ σ_k(-D^2u)=u^p\quad\text{in }\R^n,\qquad -D^2u\in\ov…
A Quantitative Pólya--Szegő Theorem for Tangential Polygons
Changfeng Gui, Yeyao Hu, Qinfeng Li
For a bounded Lipschitz domain , let denote its torsional rigidity, where in and on . We prove a quantit…
Non-radial solutions for the quasi-linear Hénon type -Laplacian Liouville equation
Wei Dai, Lixiu Duan, Changfeng Gui +1
In this paper, we investigate the following quasi-linear weighted -Laplacian Liouville equation \begin{equation*}\label{0} -Î_N u=|x|^{Nα}e^{u}, \qquad x\in \R^N, \end{equatio…
Mixed Torsion on Right Triangles and the Pólya--SzegŠMonotonicity Problem for Regular Polygons
Changfeng Gui, Yeyao Hu, Qinfeng Li +1
Motivated by the polygonal Pólya--SzegÅ conjecture for torsional rigidity, we study two monotonicity problems for torsional rigidity. The first concerns a mixed torsion problem o…
Monotonicity of the first nonzero Steklov eigenvalue of regular -gon with fixed perimeter
Zhuo Cheng, Changfeng Gui, Yeyao Hu +2
We study the first nontrivial Steklov eigenvalue of perimeter-normalized regular \(N\)-gons and show that it is strictly increasing in \(N\). The proof mainly relies on an analytic…
Nonlinear Neumann boundary problems for -Laplacian Liouville equation on a half space
Wei Dai, Changfeng Gui, Yichen Hu +1
In this paper, for general , we classify solutions to -Laplacian Liouville equation with positive nonlinear Neumann boundary condition on the half-space $\mathbb{R}^{n}_…