Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On spherical inversions of polyharmonic functions

Author: Allen T. Chwang
Journal: Quart. Appl. Math. 44 (1987), 793-799
MSC: Primary 31B30
DOI: https://doi.org/10.1090/qam/872829
MathSciNet review: 872829
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Abstract: A general spherical inversion theorem for polyharmonic functions of order $ m$ has been obtained, and it reduces to the Kelvin transformation for $ m = 1$. For biharmonic functions $ \left( {m = 2} \right)$, the present theorem has been applied to generate an explicit solution which satisfies the prescribed homogeneous boundary conditions on the surface of a sphere.

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DOI: https://doi.org/10.1090/qam/872829
Article copyright: © Copyright 1987 American Mathematical Society

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