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SUMMARY:Minimization of the first eigenvalue of the elasticity operator - 
 Antoine Henrot (Université de Lorraine)
DTSTART:20260326T114500Z
DTEND:20260326T124500Z
UID:TALK241153@talks.cam.ac.uk
DESCRIPTION:In this talk we consider the problem of determining a domain i
 n $\\R^N$ that minimizes the first eigenvalue of the elasticity (or Lam\\'
 e) system under a volume constraint. We prove existence of an optimal doma
 in. We derive first and second-order optimality conditions. Leveraging the
 se conditions\, we demonstrate that in two dimensions\, the disk cannot be
  the optimal shape when the Poisson ratio is below a specific threshold\, 
 whereas above this value\, it serves as a local minimizer. We also find so
 me explicit domains that have a lower first eigenvalue than the disk for P
 oisson ratios $\\nu \\leq 0.4$.\nThis is a joint work with Antoine Lemenan
 t and Yannick Privat
LOCATION:Seminar Room 1\, Newton Institute
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