Minimization of the buckling load of a clamped plate with perimeter constraint
Michele Carriero, Simone Cito, Antonio Leaci · arXiv (Cornell University) · 2023
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.