Nyquist frequency of partial_x*partial_y

I found out that Steven's notes on handling Nyquist frequency for
derivatives very useful:
http://math.mit.edu/~stevenj/fft-deriv.pdf

Here I have some questions that I would like some insights:
How to handle partial_x*partial_y elegantly?  Two typical cases:
1) Sometimes by transforming coordinates, a irregular grid works better --
then this partial_x*partial_y term appears.
2) The media is anisotropic.
It looks like that there always exists a local transform that will convert
the equation to be with pure 2nd order derivative, but not globally in a FD
scheme.

Thanks!

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