A Characterization of Harmonic Lr-Vector Fields in Three Dimensional Exterior Domains
A Characterization of Harmonic Lr-Vector Fields in Three Dimensional Exterior Domains
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DOI：
10.1007/s12220-022-00938-8
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发表时间：
2022-07-01
影响因子：
1.1
通讯作者：
Yanagisawa, Taku
中科院分区：
文献类型：
--
作者：
Hieber, Matthias;Kozono, Hideo;Yanagisawa, Taku
考虑L-r（Ω）中的调和向量场u的空间，其中1 < r <无穷大，对于三维外部区域Ω，具有光滑边界偏导数Ω，且边界条件u。v = 0或u x v = 0，其中v表示偏导数Ω上的单位向外法线。用X-har（r）（Omega）和V-har（r）（Omega）表示这些空间，证明了尽管Omega缺乏紧性，但这两个空间都是有限维的，并且dim V-har（r）（Omega）对于3/2
Consider the space of harmonic vector fields u in L-r (Omega) for 1 < r < infinity for three dimensional exterior domains Omega with smooth boundaries partial derivative Omega subject to the boundary conditions u . v = 0 or u x v = 0, where v denotes the unit outward normal on partial derivative Omega. Denoting these spaces by X-har(r) (Omega) and V-har(r)(Omega), it is shown that, in spite of the lack of compactness of Omega, both of these spaces are finite dimensional and that dim V-har(r) (Omega) equals L for 3/2 < r < infinity and L -1 for 1 < r