Abstract
For a solution u of Δnu = 0, where Δ is the Laplacian in m-space and n is a positive integer, we establish a transformation through inversion in the unit sphere which transforms u into a solution v of Δnv = 0. For n = 1 this is the classical Kelvin transformation and for m = n = 2 this is the Michell transformation. Applications are given to spectral theory and oscillation theory.
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© 1983 Springer-Verlag
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Ahlbrandt, C.D., Hinton, D.B., Lewis, R.T. (1983). Inversion in the unit sphere for powers of the Laplacian. In: Everitt, W.N., Lewis, R.T. (eds) Ordinary Differential Equations and Operators. Lecture Notes in Mathematics, vol 1032. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076789
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DOI: https://doi.org/10.1007/BFb0076789
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