  We propose a local regularization of elliptic optimal control problems which
involves the nonconvex $L^q$ fractional penalizations in the cost function. The
proposed \emph{Huber type} regularization allows us to formulate the PDE
constrained optimization formulation as a DC programming problem (difference of
convex functions) that is useful to obtain necessary optimality conditions and
tackle its numerical solution by applying the well known DC algorithm used in
nonconvex optimization problems. By this procedure we approximate the original
problem in terms of a consistent family of parameterized problems for which
there are efficient numerical methods available. Finally, we present numerical
experiments to illustrate our theory with different configurations associated
to the parameters of the problem.
