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Adding short description: "For a large class of boundary conditions, all solutions have the same gradient" (Shortdesc helper) |
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{{short description|For a large class of boundary conditions, all solutions have the same gradient}}
The '''uniqueness theorem''' for [[Poisson's equation]] states that, for a large class of [[boundary condition]]s, the equation may have many solutions, but the gradient of every solution is the same. In the case of [[electrostatics]], this means that there is a unique [[electric field]] derived from a potential function satisfying Poisson's equation under the boundary conditions.
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