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

31 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Stability for a GNS inequality and the log-HLS inequality, with application to the critical mass keller-segel equation'. Together they form a unique fingerprint.

  • Cite this