Existence of minimizers for the Bianchi-Egnell stability inequality


Event details

Date 15.03.2024
Hour 15:30
Speaker Dr. Tobias König (Univ. Frankfurt)
MA B1 11
Category Conferences - Seminars
Event Language English

Associated 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 optimizers.
In this talk, I will present some recent results concerning the 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 proved by exploiting symmetry and convexity properties of the associated quotient functional. The same findings apply for the fractional Sobolev inequality of order $s \in (0, d/2)$, provided that the space dimension $d$ is at least two.

If $d =1$ on the other hand, the Bianchi-Egnell has a surprising different behavior, which I will also address in my talk.

Practical information

  • General public
  • Free


  • Prof. Maria Colombo


  • Prof. Maria Colombo

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