Geodesic
Decompositions of the Sobolev Scale and Gradient–Divergence Scale into the Sum of Solenoidal and Potential Subspaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 136-145 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the complete Sobolev scale and the gradient–divergence scale, decompositions into direct sums of solenoidal and potential subspaces are found. A smoothing property of solenoidal factorization is proved. Projectors onto the subspaces of solenoidal and potential functions are described. 
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     author = {Yu. A. Dubinskii},
     title = {Decompositions of the {Sobolev} {Scale} and {Gradient{\textendash}Divergence} {Scale} into the {Sum} of {Solenoidal} and {Potential} {Subspaces}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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Yu. A. Dubinskii. Decompositions of the Sobolev Scale and Gradient–Divergence Scale into the Sum of Solenoidal and Potential Subspaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 136-145. http://geodesic.mathdoc.fr/item/TM_2006_255_a9/

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[2] Dubinskii Yu.A., “Kompleksnyi analog zadachi Neimana i ortogonalnoe razlozhenie $L_2$ v summu analiticheskogo i koanaliticheskogo podprostranstv”, DAN, 393:2 (2003), 155–158 | MR

[3] Dubinskii Yu.A., “Ob odnoi kompleksnoi kraevoi zadache”, Vestn. MEI, 2004, no. 6, 43–48

[4] Dubinskii Ju.A., “Complex Neumann type boundary problem and decomposition of Lebesgue spaces”, Discr. and Contin. Dyn. Syst., 10:1–2 (2004), 201–210 | MR | Zbl