The Lp Dirichlet problem for elliptic systems on Lipschitz domains

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35 Scopus citations


We develop a new approach to the Lp Dirichlet problem via L 2 estimates and reverse Holder inequalities. We apply this approach to second order elliptic systems and the polyharmonic equation on a bounded Lipschitz domain Ω in ℝn. For n > 4 and 2 - ε < p < 2(n-1)/n-3 + ε, we establish the solvability of the Dirichlet problem with boundary data in Lp(∂Ω). In the case of the polyharmonic equation Δlu = 0 with l ≥ 2, the range of p is sharp if 4 ≤ n < 2l + 1.

Original languageEnglish
Pages (from-to)143-159
Number of pages17
JournalMathematical Research Letters
Issue number1
StatePublished - Jan 2006


  • Dirichlet Problems
  • Elliptic Systems
  • Lipschitz Domains
  • Polyharmonic Equations

ASJC Scopus subject areas

  • Mathematics (all)


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