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SUMMARY:Existence of minimizers for the Bianchi-Egnell stability inequalit
 y
DTSTART:20240315T153000
DTSTAMP:20260916T084332Z
UID:1a67d619a6988f3c4cf74c1757d5251704974ce7d91128a6bbc2150b
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr. Tobias König (Univ. Frankfurt)\nAbstract:\nAssociated to 
 Sobolev's inequality\, the stability inequality due to Bianchi and Egnell 
 bounds the 'Sobolev deficit' of a function in terms of a constant $c_{BE} 
 > 0$ times its squared $\\dot{H}^1$-distance to the manifold of Sobolev op
 timizers.\nIn this talk\, I will present some recent results concerning th
 e Bianchi-Egnell inequality. Based on new strict upper bounds for the best
  constant $c_{BE}$\, the existence of a minimizer for $c_{BE}$ can be prov
 ed by exploiting symmetry and convexity properties of the associated quoti
 ent functional. The same findings apply for the fractional Sobolev inequal
 ity of order $s \\in (0\, d/2)$\, provided that the space dimension $d$ is
  at least two.\n\nIf $d =1$ on the other hand\, the Bianchi-Egnell has a s
 urprising different behavior\, which I will also address in my talk.
LOCATION:MA B1 11
STATUS:CONFIRMED
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