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SUMMARY:On the Courant-sharp Dirichlet eigenvalues of Euclidean sets
DTSTART:20170503T150000
DTEND:20170503T170000
DTSTAMP:20260509T175246Z
UID:a40ed1d62d385644cca760c78fd742a3ecf35317da3e9bafed6b778d
CATEGORIES:Conferences - Seminars
DESCRIPTION:Katie Gittins (Université de Neuchâtel)\nConsider an arbitra
 ry open set Omega in Euclidean space with finite Lebesgue measure.\nLet la
 mbda_k(Omega) denote the eigenvalues of the Dirichlet Laplace operator act
 ing in L^2(Omega).\nThe Dirichlet eigenvalue lambda_k(Omega) is Courant-sh
 arp if the corresponding eigenfunction has exactly k nodal domains.\n\nIn 
 the first part of the talk we give an introduction to this topic\, includi
 ng a proof of Pleijel's theorem\, and review\nsome recent results for the 
 Courant-sharp Dirichlet eigenvalues of Euclidean sets.\n\nIn the second pa
 rt of the talk we obtain an upper bound for the largest Courant-sharp Diri
 chlet eigenvalue of $\\Omega$\, and deduce an upper bound for the number o
 f Courant-sharp Dirichlet eigenvalues of $\\Omega$.\n\nThis is joint work 
 with M.  van den Berg\, and extends recent results due to P. Bérard and 
 B. Helffer.\n 
LOCATION:CE 1 105
STATUS:CONFIRMED
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