 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-3/2g/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Statement (iii) is false. On the unit disc, take

ϕ (x, y) = 1 - x^{2} - y^{2}, f = Δ ϕ = - 4.

f

is continuous on the closed disc, but

ϕ

has its strict maximum

1

at the interior point

(0, 0)

and equals zero on the boundary.

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