Sharp integral inequalities for harmonic functions

Fengbo Hang, Xiaodong Wang, Xiaodong Yan

Research output: Contribution to journalArticle

Abstract

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
Volume61
Issue number1
DOIs
StatePublished - Jan 2008

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Liouville Type Theorem
Harmonic functions
Sharp Inequality
Isoperimetric Inequality
Nonnegative Solution
Integral Inequality
Harmonic Functions
Half-space
Regularity

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Sharp integral inequalities for harmonic functions. / Hang, Fengbo; Wang, Xiaodong; Yan, Xiaodong.

In: Communications on Pure and Applied Mathematics, Vol. 61, No. 1, 01.2008, p. 54-95.

Research output: Contribution to journalArticle

Hang, Fengbo ; Wang, Xiaodong ; Yan, Xiaodong. / Sharp integral inequalities for harmonic functions. In: Communications on Pure and Applied Mathematics. 2008 ; Vol. 61, No. 1. pp. 54-95.
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