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SUMMARY:Semiclassical inequalities for Dirichlet and Neumann Laplacians - 
 Simon Larson (Göteborgs Universitet)
DTSTART:20260202T140000Z
DTEND:20260202T144500Z
UID:TALK239578@talks.cam.ac.uk
DESCRIPTION:In this talk\, we consider inequalities for the Riesz means of
  order &gamma\; for eigenvalues of Dirichlet and Neumann Laplacians. Class
 ical results due to Berezin\, Li&ndash\;Yau\, and Kr&ouml\;ger state that 
 for &gamma\; &ge\; 1\, the Riesz means are bounded by their semiclassical 
 approximation. In recent joint work with R. Frank\, we show that such ineq
 ualities extend to a range of &gamma\; <1\, under the assumption that the 
 domain is convex. I will present these extensions and discuss their implic
 ations in related shape optimization problems.\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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