 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-4/23h/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

H_{0}^{1} (Ω) = \overline{C_{c}^{\infty} (Ω)}^{H^{1} (Ω)} .

Here

H^{1} (Ω)

consists of the

L^{2}

L^{2}

, with norm

∥ u ∥_{H^{1}}^{2} = \int_{Ω} (∣ u ∣^{2} + ∣\nabla u ∣_{2}^{2}) .

On a sufficiently regular domain, the closure condition is equivalent to having zero boundary trace.

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