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

On a mixed singular/switching control problem with multiples regimes