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Math Help - Uniqeness of weak solution to variational problem

  1. #1
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    Uniqeness of weak solution to variational problem

    I have been trying to show that the weak solution  u \in H^1(\Omega) such that
     \displaystyle\int_\Omega \nabla u . \nabla v + \alpha + \displaystyle\int_{\partial\Omega} uv = \displaystyle\int_\Omega vf for all  v \in H^1(\Omega)

    is unique. I have been told this is hard. I could use Lax-Milgram to show existance and uniqueness but am finding it hard to show coercivity and continuity... any ideas... I only have to show uniqueness, not existence...
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  2. #2
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    is it something to do with showing the LHS is an inner product??
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