Maximum principles for the polyharmonic equation on Lipschitz domains

J. Pipher, G. C. Verchota

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


The Agmon-Miranda maximum principle for the polyharmonic equations of all orders is shown to hold in Lipschitz domains in ℝ3. In ℝn, n≥4, the Agmon-Miranda maximum principle and Lp-Dirichlet estimates for certain p>2 are shown to fail in Lipschitz domains for these equations. In particular if 4≤n≤2 m+1 the Lp Dirichlet problem for Δm fails to be solvable for p>2(n−1)/(n−3).

Original languageEnglish (US)
Pages (from-to)615-636
Number of pages22
JournalPotential Analysis: An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis
Issue number6
StatePublished - Dec 1995


  • 35J
  • Agmon-Miranda
  • Nonsmooth
  • dilation invariant
  • implicit functional

ASJC Scopus subject areas

  • Analysis


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