Riemann Boundary Value Problem for Triharmonic Equation in Higher Space
We mainly deal with the boundary value problem for triharmonic function with value in a universal Clifford algebra: Δ3[u](x)=0, x∈Rn∖∂Ω, u+(x)=u-(x)G(x)+g(x), x∈∂Ω, (Dju)+(x)=(Dju)-(x)Aj+fj(x), x∈∂Ω, u(∞)=0, where (j=1,…,5) ∂Ω is a Lyapunov surface in Rn, D=∑k=1nek(∂/∂xk) is the Dirac operator, and...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/415052 |
| Summary: | We mainly deal with the boundary value problem for triharmonic function with value in a universal Clifford algebra: Δ3[u](x)=0, x∈Rn∖∂Ω, u+(x)=u-(x)G(x)+g(x), x∈∂Ω, (Dju)+(x)=(Dju)-(x)Aj+fj(x), x∈∂Ω, u(∞)=0, where (j=1,…,5) ∂Ω is a Lyapunov surface in Rn, D=∑k=1nek(∂/∂xk) is the Dirac operator, and u(x)=∑AeAuA(x) are unknown functions with values in a universal Clifford algebra Cl(Vn,n). Under some hypotheses, it is proved that the boundary value problem has a unique solution. |
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| ISSN: | 2356-6140 1537-744X |