On the distributional divergence of vector fields vanishing at infinity
Published online by Cambridge University Press: 11 February 2011
Abstract
The equation div υ = F has a solution υ in the space of continuous vector fields vanishing at infinity if and only if F acts linearly on BVm/(m−1)(ℝm) (the space of functions in Lm/(m−1)(ℝm) whose distributional gradient is a vector-valued measure) and satisfies the following continuity condition: F(uj) converges to zero for each sequence {uj} such that the measure norms of ∇j are uniformly bounded and uj ⇀ 0 weakly in Lm/(m−1)(ℝm).
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 1 , February 2011 , pp. 65 - 76
- Copyright
- Copyright © Royal Society of Edinburgh 2011
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