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SUMMARY:The Laplace operator with Neumann boundary conditions under pertur
 bations of the domain (I and II)
DTSTART:20170627T153000
DTEND:20170627T173000
DTSTAMP:20261002T022049Z
UID:8099df0001e234ae07123f72686d659840d56845e63e539a2a5fcf86
CATEGORIES:Conferences - Seminars
DESCRIPTION:José Maria Arrieta (Universidad Complutense de Madrid)\nWe wi
 ll consider the Laplace operator with Neumann boundary condition and will 
 try to understand its behavior when the domain undergoes a perturbation.\n
 We will provide conditions on the perturbations under which the continuity
  of the resolvent and the spectrum of the operator is obtained. \nWe will
  also analyze in detail the case of a dumbbell domain perturbation which\,
  roughly speaking\, consists of two fixed domains joined by a thin channel
 .  The thin channel is of thickness epsilon>0 and it degenerates to a lin
 e segment as epsilon goes to 0.   We will show that\, in general\, there 
 is a net contribution to the spectral behavior of the limiting problem com
 ing from the channel and will analyze how the shape of the thin channel in
 fluences the spectral behavior of the limiting problem. We will also obtai
 n the first term in the asymptotic expansion of the eigenvalues as the thi
 ckness of the thin channel goes to 0.  If time allows\, we will show some
  extensions of these results to other situations like: other boundary cond
 itions (like Robin)\,  higher order operators (biharmonic)\,  nonlinear 
 elliptic problems and reaction diffusion equations in dumbbell domains.  
 \n 
LOCATION:MA A3 31 https://plan.epfl.ch/?room=MAA331
STATUS:CONFIRMED
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