The mixed problem for the Lamé system in a class of Lipschitz domains

Russell M. Brown, Irina Mitrea

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We consider the mixed problem for the Lamé system{(L u = 0, in Ω,; u |D = fD, on D,; frac(∂ u, ∂ ρ) = fN, on N,; (∇ u)* ∈ Lp (∂ Ω)) in the class of bounded Lipschitz creased domains. Here D and N partition ∂Ω and ∂ / ∂ ρ stands for the traction operator. We suppose the Dirichlet data fD has one derivative in Lp (D) and the traction data fN is in Lp (N). For p in a small interval containing 2, we find a unique solution to the mixed problem subject to the condition that the non-tangential maximal function of the gradient of the solution is in Lp (∂ Ω).

Original languageEnglish
Pages (from-to)2577-2589
Number of pages13
JournalJournal of Differential Equations
Volume246
Issue number7
DOIs
StatePublished - Apr 1 2009

Bibliographical note

Funding Information:
✩ Research supported in part by the NSF DMS Grant 0547944.

Keywords

  • Lamé system
  • Layer potentials
  • Lipschitz domains
  • Mixed boundary value problems
  • Well-posedness

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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