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EnglishWe 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 $\varphi (z)=- K(z,z)^{-1/(n+1)}$ of a strictly pseudoconvex bounded domain $\Omega \subset \mathbb{C}^n$ which is smooth up to the boundary must vanish on $\partial \Omega$. If $n \neq 5$ and $u T$ is a harmonic vector field with $u \in C^2(\overline{\Omega})$ then $u|_{\partial \Omega} = 0$.
http://hdl.handle.net/11563/6239| Titolo: | On the Dirichlet problem for the harmonic vector fields equation |
| Autori interni: | BARLETTA, Elisabetta |
| Data di pubblicazione: | 2007 |
| Rivista: | NONLINEAR ANALYSIS |
| Abstract: | 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 $\varphi (z)=- K(z,z)^{-1/(n+1)}$ of a strictly pseudoconvex bounded domain $\Omega \subset \mathbb{C}^n$ which is smooth up to the boundary must vanish on $\partial \Omega$. If $n \neq 5$ and $u T$ is a harmonic vector field with $u \in C^2(\overline{\Omega})$ then $u|_{\partial \Omega} = 0$. |
| Handle: | http://hdl.handle.net/11563/6239 |
| Appare nelle tipologie: | 1.1 Articolo su Rivista |
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