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Riemann boundary value problem for triharmonic equation in higher space.

Authors
  • Gu, Longfei
Type
Published Article
Journal
The Scientific World JOURNAL
Publisher
Hindawi (The Scientific World)
Publication Date
Jan 01, 2014
Volume
2014
Pages
415052–415052
Identifiers
DOI: 10.1155/2014/415052
PMID: 25114963
Source
Medline
License
Unknown

Abstract

We mainly deal with the boundary value problem for triharmonic function with value in a universal Clifford algebra: Δ(3)[u](x) = 0, x ∈ R (n)\∂Ω, u (+)(x) = u (-)(x)G(x) + g(x), x ∈ ∂Ω, (D (j) u)(+)(x) = (D (j) u)(-)(x)A j + f j (x), x ∈ ∂Ω, u(∞) = 0, where (j = 1,…, 5)  ∂Ω is a Lyapunov surface in R (n) , D = ∑ k=1 (n) e k (∂/∂x k) is the Dirac operator, and u(x) = ∑ A e A u A (x) are unknown functions with values in a universal Clifford algebra Cl(V n,n). Under some hypotheses, it is proved that the boundary value problem has a unique solution.

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