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Decompositions of the Sobolev scale and gradient-divergence scale into the sum of solenoidal and potential subspaces

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Abstract

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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References

  1. Y. Roitberg, Elliptic Boundary Value Problems in the Spaces of Distributions (Kluwer, Dordrecht, 1996), Math. Appl. 384.

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Authors and Affiliations

  1. Moscow Power Engineering Institute, Krasnokazarmennaya ul. 14, Moscow, 111250, Russia

    Yu. A. Dubinskii

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  1. Yu. A. Dubinskii
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Original Russian Text © Yu.A. Dubinskii, 2006, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Vol. 255, pp. 136–145.

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Dubinskii, Y.A. Decompositions of the Sobolev scale and gradient-divergence scale into the sum of solenoidal and potential subspaces. Proc. Steklov Inst. Math. 255, 127–135 (2006). https://doi.org/10.1134/S0081543806040109

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  • DOI: https://doi.org/10.1134/S0081543806040109

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