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CATEGORIES:Analysis seminar
SUMMARY:Bounds for the rate of change of the Sobolev const
ant - Tom Carroll (University College Cork)
DTSTART:20160222T160000Z
DTEND:20160222T170000Z
UID:TALK1940AT
URL:/talk/index/1940
DESCRIPTION:The Sobolev constant of a bounded region in Euclid
ean space decreases as the region expands. Isoperi
metric bounds for the rate of decrease of the Sobo
lev constant are obtained. These apply\, in partic
ular\, to the first Dirichlet eigenfunction of the
Laplacian and to the (inverse of the) torsional r
igdity. The main ingredients are a fairly standard
Hadamard variation formula and a reverse Holder i
nequality for the eigenfuntions. This is joint wor
k with Jesse Ratzkin and Moustapha Fall.
LOCATION:Lecture room B\, Watson building
CONTACT:Andrew Morris
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