Adams' Inequality with the Exact Growth Condition in ℝ4

Nader Masmoudi, Federica Sani

Research output: Contribution to journalArticlepeer-review


Adams' inequality is an extension of the Trudinger-Moser inequality to the case when the Sobolev space considered has more than one derivative. The goal of this paper is to give the optimal growth rate of the exponential-type function in Adams' inequality when the problem is considered in the whole space ℝ4.

Original languageEnglish (US)
Pages (from-to)1307-1335
Number of pages29
JournalCommunications on Pure and Applied Mathematics
Issue number8
StatePublished - Aug 2014

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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