Solving for a function in an equality of Laplacian operators
I want to solve the following :
Laplace(D(I(S))) = Laplace(D(G))
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.