Calculus of Variations and Geometric Measure Theory

M. Carriero - S. Cito - A. Leaci

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

created by cito1 on 25 Nov 2022
modified on 25 Jan 2024


Published Paper

Inserted: 25 nov 2022
Last Updated: 25 jan 2024

Journal: Applied Mathematics and Optimization
Year: 2024


We look for minimizers of the buckling load problem with perimeter constraint in any dimension. In dimension 2, we show that the minimizing plates are convex; in higher dimension, by passing through a weaker formulation of the problem, we show that any optimal set is open and connected. For higher eigenvalues, we prove that minimizers exist among convex sets with prescribed perimeter.

Keywords: shape optimization, perimeter constraint, buckling eigenvalues, bilaplacian operator