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Existence of $H^{1/2}(\partial\Omega)$-regular unit tangent field on smooth surface
Suppose that $\Omega$ is a bounded, smooth, simply connected domain in $\mathbb{R}^3$. My goal is to show that there is a $p(x) \in H^1(\Omega,\mathbb{S}^2)$ such that $p(x)$ lies on the tangent plane ...
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