Solving Laplace's Equation with Exponential Function

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- exp(f) = Laplacian(f)

where f is a real valued function of two variables in an open domain.
 
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That's certainly NOT a "simple" PDE. It is very badly non-linear.
 
HallsofIvy said:
That's certainly NOT a "simple" PDE. It is very badly non-linear.

Ok. How would I go about understanding it?