  This paper is concerned with the existence and regularity of mininizers as
well as of corresponding multipliers to an optimal control problem governed by
semilinear elliptic equations, in which mixed pointwise control-state
constraints are considered in a quite general form and the controls act
simultaneously in the domain and on the boundary. Under standing assumptions,
the minimizers and the corresponding multipliers do exist. Furthermore, by
applying the bootstrapping technique and establishing some calculation tools
for functions in Sobolev spaces of fractional order, the optimal solutions and
the associated Lagrange multipliers are shown to be Lipschitz continuous.
