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15 February 2013 Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller–Segel equation
Eric A. Carlen, Alessio Figalli
Duke Math. J. 162(3): 579-625 (15 February 2013). DOI: 10.1215/00127094-2019931

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 (GNS) inequality in the plane. Then, exploiting the connection between this inequality and a fast diffusion equation, we get stability for the logarithmic Hardy–Littlewood–Sobolev (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. "Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller–Segel equation." Duke Math. J. 162 (3) 579 - 625, 15 February 2013. https://doi.org/10.1215/00127094-2019931

Information

Published: 15 February 2013
First available in Project Euclid: 14 February 2013

zbMATH: 1307.26027
MathSciNet: MR3024094
Digital Object Identifier: 10.1215/00127094-2019931

Subjects:
Primary: 15A45
Secondary: 49M20

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 3 • 15 February 2013
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