Abstract. We present some results for systematic generation of biharmonic functions that are not readily obtainable by a direct application of the separation of variable technique to the biharmonic equation. Almansi's theorem and the Kelvin transformation were adapted to obtain the results, and they are presented as theorems followed by simple proofs. The results are not only labour-saving, but also have important implications for the construction of solutions to boundary value problems involving composite media with curved geometry.

Received: May 11, 2012

AMS Subject Classification: 31B30

Key Words and Phrases: systematic generation, harmonic, biharmonic functions, Almansi's theorem, Kelvin transformation

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