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SUMMARY:Robin and Cheeger partitions of domains - James Kennedy (Universid
 ade de Aveiro)
DTSTART:20260205T140000Z
DTEND:20260205T144500Z
UID:TALK239839@talks.cam.ac.uk
DESCRIPTION:We study the problem of partitioning domains by minimising fun
 ctionals based on Robin Laplacian eigenvalues of the partition cells\, ana
 logous to the "classical" spectral minimal partition (SMP) problems using 
 Dirichlet Laplacian eigenvalues considered by Helffer\, Terracini and othe
 rs.\nAfter a brief discussion of the history of the problem and existence 
 and well-posedness results\, we will show that\, as the parameter $\\alpha
 $ appearing in the boundary condition tends to zero\, the minimal partitio
 ns converge (up to subsequences) to a minimal partition for the correspond
 ing Cheeger partition problem\, where the functional is based on a purely 
 geometric quantity (the Cheeger constant) related to the isoperimetric rat
 io of the partition cells. This also has some interesting consequences for
  the eigenvalues of the Robin problem\, for example as regards (a lack of)
  domain monotonicity.\nThis talk will be based on an ongoing joint project
  with P&ecirc\;dra Andrade\, Nuno Carneiro\, Matthias Hofmann\, and Hugo T
 avares\, and (finished) work with Jo&atilde\;o Ribeiro\, in which we prove
  analogous results on metric graphs in place of domains.
LOCATION:Seminar Room 1\, Newton Institute
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