Stability for a GNS inequality and the log-HLS inequality, with application to the critical mass keller-segel equation

Eric A. Carlen, Alessio Figalli

Research output: Contribution to journalArticle

29 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)579-625
Number of pages47
JournalDuke Mathematical Journal
Volume162
Issue number3
DOIs
StatePublished - Feb 1 2013

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Gagliardo-Nirenberg Inequalities
Sobolev Inequality
Hardy-Littlewood Inequality
Fast Diffusion Equation
Convergence Results
Deduce
Logarithmic
Estimate

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Stability for a GNS inequality and the log-HLS inequality, with application to the critical mass keller-segel equation. / Carlen, Eric A.; Figalli, Alessio.

In: Duke Mathematical Journal, Vol. 162, No. 3, 01.02.2013, p. 579-625.

Research output: Contribution to journalArticle

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