Calculus of Variations and Geometric Measure Theory

E. Carlen - A. Figalli

Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation

created by figalli on 18 Jul 2012


Accepted Paper

Inserted: 18 jul 2012
Last Updated: 18 jul 2012

Journal: Duke Math. J.
Year: 2012


Starting from the quantitative stability result of Bianchi and Egnell for the $2$-Sobolev inequality, we deduce several different stability results for a Gagliardo-Nirenberg-Sobolev inequality in the plane. Then, exploiting the connection between this inequality and a fast diffusion equation, we get stability for the Log-HLS inequality. Finally, using all these estimates, we prove a quantitative convergence result for the critical mass Keller-Segel system.