The conformal plate buckling equation

微分形式上的屈曲与夹紧板问题

The Buckling and Clamped Plate Problems on Differential Forms

本文研究了微分形式上的屈曲与夹紧板问题，推导了其最小特征值并推广了Hodge拉普拉斯算子的估计。

Existence of an optimal domain for the buckling load of a clamped plate with prescribed volume

We formulate the minimization of the buckling load of a clamped plate as a free boundary value problem with a penalization term for the volume constraint. As the penalization parameter becomes small we show that the optimal shape problem with prescribed volume is solved. In addition, we discuss two different choices for the penalization term.

On the optimal domain for minimizing the buckling load of a clamped plate

We prove the existence of an optimal domain for minimizing the buckling load among all, possibly unbounded, open subsets of $\mathbb{R}^n$ ($n\geq 2$) with given measure. Our approach is based on the extension of a 2-dimensional existence result of Ashbaugh and Bucur and on the idea of Alt and Caffarelli to focus on the eigenfunction.

具有周长约束的固支板屈曲载荷的最小化

Minimization of the buckling load of a clamped plate with perimeter constraint

本文研究任意维度下带周长约束的屈曲载荷最小化问题，证明二维最小化板为凸集，高维最优集合为开连通集，并证明高阶特征值在指定周长的凸集族中存在最小化子。

Modeling suspension bridges through the von Kármán quasilinear plate equations

A rectangular plate modeling the deck of a suspension bridge is considered. The plate may widely oscillate, which suggests to consider models from nonlinear elasticity. The von Kármán plate model is studied, complemented with the action of the hangers and with suitable boundary conditions describing the behavior of the deck. The oscillating modes are determined in full detail. Existence and multiplicity of static equilibria are then obtained under different assumptions on the strength of the buckling load.

四阶Alt-Caffarelli问题的边界正则性及其在最小化临界屈曲载荷中的应用

Boundary regularity of a fourth order Alt-Caffarelli problem and applications to the minimization of the critical buckling load

本文研究了四阶Alt-Caffarelli问题的边界正则性，通过改进的单调性公式和epiperimetric不等式，得出了最优形状在临界屈曲载荷最小化中的正则性结果。