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Let $\Omega$ be an open domain, and let $\Sigma$ be a smooth and nonempty portion of the boundary. Let $u$ be a harmonic function in $\Omega$ and $u=D_\nu u=0$ on $\Sigma$. ($D_\nu$ is the derivative along the outward vector). How to prove $u=0$ in $\Omega$?

Can I use Green's formula to this "portion" of boundary?

user103402
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Yourent
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  • A standard argument should be using a line integral to prove $u=0$ on a small neighborhood of $\Sigma$, then apply unique continuation. – Shuhao Cao Nov 17 '13 at 16:50

1 Answers1

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A couple solutions are given here. What do you mean by using Green's formula to a "portion"?

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timur
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