  We characterize all semigroups $(T(t))_{t\geq0}$ on $L^2(\Omega)$ sandwiched
between Dirichlet and Neumann ones, i.e.: \begin{equation*}\label{eq:san}
  e^{t\Delta_D}\leq T(t)\leq e^{t\Delta_N}\quad,\text{for all }t\geq0
\end{equation*} in the positive operators sense. The proof uses the well-known
Beurling-Deny and Lejan formula to drop the locality assumption made usually on
the form associated with $(T(t))_{t\geq 0}$.
