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For questions involving the trace of a square matrix, i.e. the sum of the elements on the main diagonal.
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A distributional normal derivative for functions in $H^1(\Omega)$
It is not possible to define a normal derivative for all $u \in H^1(\Omega)$ which depends continuously on $u$.
The reason is that all $C_c^\infty(\Omega)$ is dense in $H^1_0(\Omega)$, but all $u \in …