In this paper, the problem of state and input constrained control is addressed with multidimensional constraints. We obtain a local description of the boundary of the admissible subset of the state space where the state and input constraints can be satisfied for all times. This boundary is made of two disjoint parts: the subset of the state constraint boundary on which there are trajectories pointing toward the interior of the admissible set or tangentially to it, and a barrier, namely, a semipermeable surface which is constructed via a minimum-like principle.