The poisson equation with weights in exterior domains of Rn
The poisson equation with weights in exterior domains of Rn
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DOI：
10.1080/00036819208840057
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发表时间：
1992
影响因子：
1.1
通讯作者：
W. Varnhorn
中科院分区：
文献类型：
--
作者：
W. Varnhorn
我们考虑G中的Poisson方程，其Dirichlet边界条件u=Φ在G上。这是一个具有光滑紧边界的外部区域[BLOG]。本文证明了在抛物化的Soboley空间中解u的存在唯一性。在这里，平衡条件feL ρ（G）是必要的，并且对应于f的某种衰减行为。我们证明u趋于零，|X| → ∞，如果r > n。这一结果可以应用于加权版本的泊松方程，并导致有关的声明衰减率的解决方案
We consider Poisson's equation in G with Dirichlet boundary condition u=Φ on ∂G. Here is an exterior domain with a smooth compact boundary [∂G]. In the present paper we prove existence and uniqueness of the solution u in the Soboley space parovided . Here the aditional condition f e Lρ(G) is necessary and corresponds to a certain decay behaviour of f. We show that u tends to zero as |x| → ∞ if r > n. This result can be applied to weighted versions of Poisson's equation and leads to statements about the rate of decay of the solution