If $u_1,u_2$ solve the same <Dirichlet problem>, their difference $v=u_1-u_2$ satisfies
$$
Lv=0\text{ in }\Omega,
\qquad
v=0\text{ on }\partial\Omega.
$$
Part 2(ii) applied to $v$ gives $v\leq0$, and applied to $-v$ gives $v\geq0$. Hence $v=0$ and \b[the solution is unique].

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 107 / 2 / iv / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-107/2/iv/solution