On the Dirichlet problem for the harmonic vector fields equation

We show that any harmonic (with respect to the Bergman metric) vector field tangent to the Levi distribution of the foliation by level sets of the defining function φ ( z ) = − K ( z , z ) − 1 / ( n + 1 ) of a strictly pseudoconvex bounded domain Ω ⊂ C n which is smooth up to the boundary must vanis...

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Bibliographic Details
Published in:Nonlinear analysis 2007-09, Vol.67 (6), p.1831-1846
Main Author: Barletta, Elisabetta
Format: Article
Language:English
Subjects:
Bergman metric
Dirichlet problem
Exact sciences and technology
Harmonic vector field
Mathematical analysis
Mathematics
Sciences and techniques of general use
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Summary:We show that any harmonic (with respect to the Bergman metric) vector field tangent to the Levi distribution of the foliation by level sets of the defining function φ ( z ) = − K ( z , z ) − 1 / ( n + 1 ) of a strictly pseudoconvex bounded domain Ω ⊂ C n which is smooth up to the boundary must vanish on ∂ Ω . If n ≠ 5 and u T is a harmonic vector field with u ∈ C 2 ( Ω ¯ ) then u | ∂ Ω = 0 .
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2006.08.026