  This paper studies {a} mixed singular/switching stochastic control problem
for a multidimensional diffusion with multiples regimes on a bounded domain.
Using probabilistic, partial differential equation (PDE) and penalization
techniques, we show that the value function associated with this problem agrees
with the solution to a Hamilton-Jacobi-Bellman (HJB) equation. In that way, we
see that the regularity of the value function is
$C^{0,1}\cap\W^{2,\infty}_{loc}$.
