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Like a heat equation but for functions without time dependence, space-only.
TODO confirm: does the solution of the heat equation always converge to the solution of the Laplace equation as time tends to infinity?
In one dimension, the Laplace equation is boring as it is just a straight line since the second derivative must be 0. That also matches our intuition of the limit solution of the heat equation.
Uniqueness: Uniqueness theorem for Poisson's equation.