Higher order Adams' inequality with the exact growth condition

Nader Masmoudi, Federica Sani

Research output: Contribution to journalArticlepeer-review


Adams' inequality is the complete generalization of the Trudinger-Moser inequality to the case of Sobolev spaces involving higher order derivatives. The failure of the original form of the sharp inequality when the problem is considered on the whole space Rn served as a motivation to investigate in the direction of a refined sharp inequality, the so-called Adams' inequality with the exact growth condition. Due to the difficulties arising in the higher order case from the lack of direct symmetrization techniques, this refined result is known to hold on first- and second-order Sobolev spaces only. We extend the validity of Adams' inequality with the exact growth to higher order Sobolev spaces.

Original languageEnglish (US)
Article number1750072
JournalCommunications in Contemporary Mathematics
Issue number6
StatePublished - Sep 1 2018


  • Adams inequalities
  • Best constants
  • Limiting Sobolev embeddings

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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