Michele Carriero, Simone Cito, Antonio Leaci
Published 2023-07-06Version 1
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.
Minimization of $λ_2(Ω)$ with a perimeter constraint
Minimization of the $k$ -th eigenvalue of the Robin-Laplacian with perimeter constraint
An inequality à la Szegő-Weinberger for the $p-$Laplacian on convex sets
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