[Transform the Laplacian operator into polar coordinates]
The Laplace operator is written using the covariant derivative as follows :
This can also be expressed using "div" and "grad"
Here, we transform grad(f) from Cartesian coordinates to curved coordinates
Thus, both are transformed under the same form, we can see that grad(f) is represented by a simple derivative, d(f).
Then, div(A) takes the following form in curved coordinates.
Here, as we expand Christoffel's symbol
It can express using root(g) (g is the determinant of gy, as the jacobian square)
Finally, substituting the results from (B) and (C) to (A) and use
we get
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