Sharp integral inequalities for harmonic functions

Fengbo Hang, Xiaodong Wang, Xiaodong Yan

Research output: Contribution to journalArticlepeer-review


Motivated by Carleman's proof of isoperimetric inequality in the plane, we study some sharp integral inequalities for harmonic functions on the upper half-space. We also derive the regularity for nonnegative solutions of the associated integral system and some Liouville-type theorems.

Original languageEnglish (US)
Pages (from-to)54-95
Number of pages42
JournalCommunications on Pure and Applied Mathematics
Issue number1
StatePublished - Jan 2008

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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