In this note on PDE, which is based on Evans's Partial Differentail Equations, it is said that the range of the trace map on $H^1(\Omega)$ for a smooth domain $\Omega$ is $H^{1/2}(\partial \Omega)$. Could anybody come up with a reference regarding a precise definition of $H^{1/2}(\partial \Omega)$ and the result why it is the range of the trace map?
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