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Question: Powers of Laplace-Beltrami Operator

Question:Powers of Laplace-Beltrami Operator

fernandonobrega 50 Maple
December 09 2015
2

Hello,

 

I want to compute powers of the Laplace-beltrami operator in some surface (e.g. cylinder):

 

https://en.wikipedia.org/wiki/Laplace_operator#Coordinate_expressions

 

and evaluate it for a given scalar function on the surface (e.g. a function on the cylinder).  I'm wondering if I only have to write the laplace-beltrami operator and then compute a simple power of it, or if I have to take care and compute the powers of the Laplace-beltrami operator first and then evaluate at the function on the cylinder. If the second option is the correct one (I think so), how can I compute that with maple? There is some trick way to compute powers of differential operators?

 

Thanks,

Fernando
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