Re: find f(r)
Nabla f = 0 is a very famous operation in mathematical physics.
You can solve the equation analytically, if you restrict
the problem in orthogonal coordinate systems
(i.e. rectangular, cylindrical, spherical, elliptical, etc.)
otherwise you should take numerical approach (finite difference,
finite element or others).
If you are talking about electromagnetics, the books
Fields and Waves in Electromagnetics by D.K. Cheng and
Numerical Electromagnetics by M. Sadiku
can give you quantitative and qualitative informations
regards