Gradient stability for the Sobolev inequality: The case p ≥ 2

Alessio Figalli, Robin Neumayer

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We prove a strong form of the quantitative Sobolev inequality in Rn for p ≥ 2, where the deficit of a function u ∈ W 1,p controls k∇u−∇vkLp for an extremal function v in the Sobolev inequality.

Original languageEnglish (US)
Pages (from-to)319-354
Number of pages36
JournalJournal of the European Mathematical Society
Issue number2
StatePublished - 2019


  • Quantitative inequalities
  • Sobolev inequality
  • Stability

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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