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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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where <math>S_i</math> are boundary surfaces specified by boundary conditions.
Since <math>\varepsilon > 0</math> and <math>(\mathbf{\nabla}\varphi)^2 \ge 0</math>, then <math>\mathbf{\nabla}\varphi</math> must be zero everywhere (and so <math>\mathbf{\nabla}\varphi_1 = \mathbf{\nabla}\varphi_2</math>) when the surface integral vanishes. [The English here is very poor. Page in need of improvement.]
This means that the gradient of the solution is unique when
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