Remark on the Helmholtz decomposition in domains with noncompact boundary
Remark on the Helmholtz decomposition in domains with noncompact boundary
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DOI：
10.1007/s00208-014-1033-7
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发表时间：
2013-07
影响因子：
1.4
通讯作者：
Yasunori Maekawa;H. Miura
中科院分区：
文献类型：
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作者：
Yasunori Maekawa;H. Miura
设是一个区域，其边界给定为一致Lipschitz图。对于这样一个区域，我们知道Helmholtz分解并不总是有效的，除了能量空间。本文证明了Helmholtz分解在某些各向异性空间中仍然成立，这些空间包括变量中缓慢衰减的向量场。特别地，这些类包括一些无限能量向量场。为此，我们开发了一种新的方法的基础上的因子分解的散度型椭圆算子的系数是独立的一个变量。
Letbe a domain inwhose boundary is given as a uniform Lipschitz graphfor. For such a domain, it is known that the Helmholtz decomposition is not always valid inexcept for the energy space. In this paper we show that the Helmholtz decomposition still holds in certain anisotropic spaces which include vector fields decaying slowly in thevariable. In particular, these classes include some infinite energy vector fields. For the purpose, we develop a new approach based on a factorization of divergence form elliptic operators whose coefficients are independent of one variable.