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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A classical Perron method for existence of smooth
solutions to boundary value and obstacle problems
for boundary-degenerate elliptic operators via hol
omorphic m - Feehan\, P (Rutgers\, The State Unive
rsity of New Jersey)
DTSTART;TZID=Europe/London:20140626T105000
DTEND;TZID=Europe/London:20140626T112000
UID:TALK53191AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53191
DESCRIPTION:We prove existence of solutions to boundary value
problems and obstacle problems for degenerate-elli
ptic\, linear\, second-order partial differential
operators with partial Dirichlet boundary conditio
ns using a new version of the Perron method. The e
lliptic operators considered have a degeneracy alo
ng a portion of the domain boundary which is simil
ar to the degeneracy of a model linear operator id
entified by Daskalopoulos and Hamilton (1998) in t
heir study of the porous medium equation or the de
generacy of the Heston operator (Heston\, 1993) in
mathematical fi nance. Our Perron method relies o
n weak and strong maximum principles for degenerat
e-elliptic operators\, concepts of continuous subs
olutions and supersolutions for boundary value and
obstacle problems for degenerate-elliptic operato
rs\, and maximum and comparison principle estimate
s previously developed by us.\n\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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