uniqueness theorm details
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The uniqueness theorem for Poisson's equation states that the equation has a unique gradient of the solution for a large class of boundary conditions. In the case of electrostatics, this means that if an electric field satisfying the boundary conditions is found, then it is the complete electric field.
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Princemilan:
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A uniqueness theorem / proof is, at least within mathematics of differential equations, often combined with an existence theorem / proof to a combined existence and uniqueness theorem.
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