Colloque des sciences mathématiques du Québec

28 novembre 2008 de 16 h 00 à 18 h 00 (heure de Montréal/Miami) Sur place

Shape optimization for low eigenvalues of the Laplace operator

Colloque par Alexandre Girouard (Université Laval)

This talk will be a survey of some classical problems on the spectrum of bounded planar domains and closed surfaces. The question to know which domain (if it exists!) minimizes --or maximizes-- a given eigenvalue of the Laplace operator is an old one. It can be traced back to Lord Rayleigh's book --The theory of sound-- published in 1877, where it was conjectured that the fundamental frequency of a drum is minimal when the drumhead is circular. A lot of progress has been made in the field of shape optimization since then, but many surprisingly simple questions still remain unsolved to this day. By the end of this talk, I hope to convince (at least some of you that these are rather interesting problems.


UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214