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Suppose that ? ? R n is bounded, and path-connected, and u ? C2 (?) ?...

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Advance Math

Suppose that ? ? R n is bounded, and path-connected, and u ?C2 (?) ? C(??) satisfies ( ??u = 0 in ?, u = g on ??.Prove that if g ? C(??) with g(x) = ( ? 0 for all x ? ??, > 0for some x ? ??, then u(x) > 0 for all x ? ?

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