Area integral estimates for the biharmonic operator in lipschitz domains

Jill Pipher, Gregory Verchota

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

Let D ⊆ Rn be a Lipschitz domain and let u be a function biharmonic in D, i.e., ΔΔu = 0 in D. We prove that the nontangential maximal function and the square function of the gradient of u have equivalent Lp(dµ) norms, where d µ ϵ A(do) and dσ is surface measure on ∂D.

Original languageEnglish (US)
Pages (from-to)903-917
Number of pages15
JournalTransactions of the American Mathematical Society
Volume327
Issue number2
DOIs
StatePublished - Oct 1991

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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