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The Helmholtz–Weyl decomposition in weighted Sobolev spaces

✍ Scribed by Wojciech M. Zaja̧czkowski

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
133 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by M. Lachowicz

Let f ∈ L 2,-l (R 3 ), where

We prove the decomposition f =-∇u+g, with g divergence free and u is a solution to the problem in R 3

Since f, u, g are defined in R 3 we need a sufficiently fast decay of these functions as |x|→∞.

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