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arXiv · 1107.5976

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

Eric A. Carlen·Alessio Figalli
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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 a quantitative 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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Eric A. Carlen, Alessio Figalli. 2011-07-29. Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation. https://doi.org/10.1215/00127094-2019931

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