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There is a result in a paper I am reading :

Let $\Omega$ be a bounded domain. For any $\epsilon > 0$, there is a constant $C(\epsilon)$ such that $$\lVert n \times u\rVert_{H^{-1/2}(\partial \Omega)} \leq \epsilon\lVert \nabla \times u\rVert_{L^2(\Omega)} + C(\epsilon)\lVert u\rVert_{L^2(\Omega)} $$ where $n$ is the normal.


The proof provided : For any $\phi \in H^{1/2}(\partial \Omega) $, consider the problem $$\nabla \times (\nabla \times w) + \frac{1}{\epsilon^2}w = 0 \text{ in } \Omega $$ $$ -n \times (n \times w) = \phi \text{ on } \partial \Omega$$


Could someone provide more information?

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You may want to provide the name of the paper. –  Atsushi Kanazawa Apr 4 '13 at 8:06

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