Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 2H / iii / Solution

The assertion is false. On the open unit disk take, for $0<\epsilon <1$,Its relevant fourth derivatives satisfyNevertheless, since $x^4+y^4\le (x^2+y^2{)}^2$, every point with $0<x^2+y^2\le 1$ hasThus the maximum lies strictly inside $\Omega$.

Solved by gpt-5.6-sol high.