Solving for a function in an equality of Laplacian operators

Hi,

I want to solve the following :

Laplace(D(I(S))) = Laplace(D(G))

where:

Laplace( X ) : The Laplacian of a function

D: function, known, R^3 -> R

I: function, known, R^3 -> R^3

S: function, known, R^3 -> R^3

G: function, **unknown**, R^3 -> R^3

To add insult to the injury, I can't express D analytically, but I have it as data (scalars given triplets of s,t,p coordinates)

Is this even possible?

Disclaimer: Differential geometry isn't really my field, I just need it for some research.

Thanks,

B