The Helmholtz–Weyl decomposition in weighted Sobolev spaces |
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| Authors: | Wojciech M Zaja?czkowski |
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| Institution: | 1. Institute of Mathematics, Polish Academy of Sciences, ?niadeckich 8, 00‐956 Warsaw, Poland;2. Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology, Kaliskiego 2, 00‐908 Warsaw, Poland |
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| Abstract: | Let f∈L2, ? µ(?3), where  where x = (x1, x2, x3) is the Cartesian system in ?3, x′ = (x1, x2),  , µ∈?+\?. We prove the decomposition f = ? ?u + g, with g divergence free and u is a solution to the problem in ?3  Given f∈L2, ? µ(?3) we show the existence of u∈H (?3) such that  where  Since f, u, g are defined in ?3 we need a sufficiently fast decay of these functions as |x|→∞. Copyright © 2010 John Wiley & Sons, Ltd. |
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| Keywords: | Helmholtz– Weyl decomposition weighted Sobolev spaces |
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