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- Jun 20, 2014

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I'm stepping in for
Ackbach
temporarily until he returns. Here is this week's POTW:

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Suppose $D$ is a compact domain of $\Bbb R^3,$ $F : D \to \Bbb R^3$ is continuous, and $\phi_1, \phi_2 : D \to \Bbb R$ are $C^2$-solutions of the PDE $\nabla^2 \phi = F$. If $\dfrac{\partial \phi_1}{\partial n} = \dfrac{\partial \phi_2}{\partial n}$ on the boundary $\partial D$ and $\phi_1(x_0) = \phi_2(x_0)$ for some $x_0\in \partial D,$ show that $\phi_1 = \phi_2$.

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Remember to read the POTW submission guidelines to find out how to submit your answers!

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Suppose $D$ is a compact domain of $\Bbb R^3,$ $F : D \to \Bbb R^3$ is continuous, and $\phi_1, \phi_2 : D \to \Bbb R$ are $C^2$-solutions of the PDE $\nabla^2 \phi = F$. If $\dfrac{\partial \phi_1}{\partial n} = \dfrac{\partial \phi_2}{\partial n}$ on the boundary $\partial D$ and $\phi_1(x_0) = \phi_2(x_0)$ for some $x_0\in \partial D,$ show that $\phi_1 = \phi_2$.

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Remember to read the POTW submission guidelines to find out how to submit your answers!

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