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P-separation of variables in Laplace's equation

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Abstract

The P-separation of variables in Laplace's equation Δ2u = 0 in flat n-dimensional space Sn is proved to be equivalent to the complete separation of variables in the invariant Laplace equation

$$\Delta u \equiv \left\{ {\Delta _2 + \frac{{n - 2}}{{4(n - 1)}}R} \right\}u = 0$$

, in a space Vn of constant curvature K ≠ 0 (Δ is the invariant Laplacian, and R is the scalar curvature, all in Vn).

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Authors and Affiliations

  1. P. N. Lebedev Physics Institute, Academy of Sciences of the USSR, USSR

    I. I. Tugov

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  1. I. I. Tugov
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Translated from Matematicheskie Zametki, Vol. 8, No. 1, pp. 121–127, July, 1970.

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Tugov, I.I. P-separation of variables in Laplace's equation. Mathematical Notes of the Academy of Sciences of the USSR 8, 538–541 (1970). https://doi.org/10.1007/BF01093449

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  • DOI: https://doi.org/10.1007/BF01093449

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