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I came across this post from the computational science board: https://scicomp.stackexchange.com/questions/26495/well-posedness-of-elasticity-boundary-conditions

I agree with the posted answer, but I am wondering if there should be an additional condition on the bottom side, such that $\sigma_n=C$ at the bottom? This would give the problem an explicit balance of forces, but I don't know if this is needed?

If the problem is solved without this additional constraint, could it be possible that $\sigma_n$ at the bottom side end up $\neq C$?

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