Accepted Paper

Inserted: 18 jul 2012
Last Updated: 18 jul 2012

Journal: Duke Math. J.
Year: 2012

Abstract:

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.

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