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DTSTAMP:20240913T045041Z
UID:1675350900@ist.ac.at
DTSTART:20230202T161500
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DESCRIPTION:Speaker: Giovanni Brigati\nhosted by Jan Maas\nAbstract: The in
terest for Sobolev's inequalites on the Euclidean space started in the 20t
h century\, after the works of Sobolev\, Gagliardo\, and Nirenberg. Optima
l constants and functions were computed by Aubin and Talenti in the 80's.
Then\, Brezis and Lieb conjectured that the deficit (say\, the difference
between the two sides) of the inequality could control some distance from
the set of optimisers. A first result for Sobolev's inequality\, due to Bi
anchi and Egnell\, appeared in the 90s. In the subsequent decades\, more a
nd more work has been devoted to stability issues\, and in particular to S
obolev's inequality. Sobolev's inequality rewrites equivalently on the sph
ere\, and the known stability results apply thoroughly. Much less was know
n about Gagliardo-Nirenberg inequalities on the sphere (i.e. the subcritic
al family interpolating between Sobolev's and PoincarĂ© inequalities)\, un
til a recent paper by Rupert Frank.Inspired by the last contribution\, a r
ather complete theory - with constructive stability estimates - has been e
stabished by Dolbeault\, Simonov\, and the speaker. The main results and t
echniques of such theory will be the subject of my talk.
LOCATION:Mondi 2\, I01.01.008\, Central Building\, ISTA
ORGANIZER:
SUMMARY:Giovanni Brigati: Constructive stability for subcritical inequaliti
es on the sphere and beyond
URL:https://talks-calendar.ista.ac.at/events/3968
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