The Lp boundary value problems on Lipschitz domains

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Abstract

Let Ω be a bounded Lipschitz domain in Rn. We develop a new approach to the invertibility on Lp (∂ Ω) of the layer potentials associated with elliptic equations and systems in Ω. As a consequence, for n ≥ 4 and frac(2 (n - 1), (n + 1)) - ε < p < 2 where ε > 0 depends on Ω, we obtain the solvability of the Lp Neumann type boundary value problems for second order elliptic systems. The analogous results for the biharmonic equation are also established.

Original languageEnglish
Pages (from-to)212-254
Number of pages43
JournalAdvances in Mathematics
Volume216
Issue number1
DOIs
StatePublished - Dec 1 2007

Bibliographical note

Funding Information:
1 The author is supported in part by the NSF (DMS-0500257).

Keywords

  • Biharmonic equation
  • Dirichlet problem
  • Elliptic systems
  • Lipschitz domains
  • Neumann problem

ASJC Scopus subject areas

  • General Mathematics

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