Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 105 / 2 / c / Solution

For a bounded open $U\subset\mathbb R^n$, $m^2>0$, and $f\in L^2(U)$, there is a unique $u\in H_0^1(U)$ such that
$$
\int_U(\nabla u\cdot\nabla v+m^2uv)
=\int_Ufv
$$
for every $v\in H_0^1(U)$.


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 Incoming links: Weak Dirichlet problem for the massive Laplacian