Maximum principles for the polyharmonic equation on Lipschitz domains

J. Pipher, Gregory Verchota

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25 Scopus citations

Abstract

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).

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Keywords

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

ASJC Scopus subject areas

  • Analysis

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