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.

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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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     title = {Decompositions of the {Sobolev} {Scale} and {Gradient--Divergence} {Scale} into the {Sum} of {Solenoidal} and {Potential} {Subspaces}},
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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/

[1] Roitberg Y., Elliptic boundary value problems in the spaces of distributions, Math. and Its Appl., 384, Kluwer, Dordrecht, 1996 | MR | Zbl

[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