Optimality conditions for the buckling of a clamped plate

2014/08/29 by Knappmann, Kathrin, Wagner, Alfred · 1 citation
#35J20 #35N25 #49K20 #49R05 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1408.6982

Abstract

We prove the following uniqueness result for the buckling plate. Assume there exists a smooth domain which minimizes the first buckling eigenvalue for a plate among all smooth domains of given volume. Then the domain must be a ball. The proof uses the second variation for the buckling eigenvalue and an inequality by L. E. Payne to establish this result.

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