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

@article{Stollenwerk2021ExistenceOA,
  title={Existence of an optimal domain for the buckling load of a clamped plate with prescribed volume},
  author={Kathrin Stollenwerk},
  journal={Annali di Matematica Pura ed Applicata (1923 -)},
  year={2021}
}
  • Kathrin Stollenwerk
  • Published 14 October 2021
  • Mathematics
  • Annali di Matematica Pura ed Applicata (1923 -)
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. 

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