Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 23H / e / Solution

No. Point evaluation is continuous on $H^1(\mathbb{R})$, and every limit of functions supported away from zero has trace $u(0)=0$. A smooth function with nonzero value at zero belongs to $H^1$ but not to this $H_0^1$.

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