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PRODID:-//Memento EPFL//
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SUMMARY:Upper bounds for Courant-sharp Neumann eigenvalues
DTSTART:20181128T143000
DTEND:20181128T153000
DTSTAMP:20260406T142516Z
UID:ddcfa1784e9815720acd182febfa988aa0734dc6f925c92fda0661c0
CATEGORIES:Conferences - Seminars
DESCRIPTION:Katie Gittins\,  Maître-assistante à l'Institut de Mathém
 atiques de l'Université de Neuchâtel\nLet $\\Omega$ be an open\, bounded
 \, connected set in $\\R^n$\, $n \\geq 2$\, with Lipschitz boundary.\nWe c
 onsider the eigenvalues of the Neumann Laplacian acting in $L^2(\\Omega)$.
 \nIn particular\, those that have a corresponding eigenfunction which achi
 eves\nequality in Courant's Nodal Domain theorem.\nThese eigenvalues are c
 alled Courant-sharp.\n\nIt was shown recently by C. Léna that an open\, b
 ounded\, connected set in $\\R^n$\, $n \\geq 2$\,\nwith $C^{1\,1}$ boundar
 y has finitely many Courant-sharp Neumann eigenvalues.\n\nWe discuss upper
  bounds for the Courant-sharp Neumann eigenvalues of the Laplacian\nof an 
 open\, bounded\, connected set in $\\R^n$\, $n \\geq 2$\, with $C^2$ bound
 ary.\nIn the case where the set is also convex\, we present explicit upper
  bounds for\nthe Courant-sharp Neumann eigenvalues and the number of Coura
 nt-sharp Neumann\neigenvalues in terms of some of the geometric quantities
  of the set.\n\nThis is based on joint work with Corentin Léna (Stockholm
  University).\n 
LOCATION:MA B2 485 https://plan.epfl.ch/?room=MAB2485
STATUS:CONFIRMED
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