Weak Dirichlet problem for the massive Laplacian
= Weak Dirichlet problem for the massive Laplacian
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 $v\in H_0^1(U)$.