  Optimal control problems for semilinear elliptic equations with control costs
in the space of bounded variations are analysed. BV-based optimal controls
favor piecewise constant, and hence 'simple' controls, with few jumps.
Existence of optimal controls, necessary and suffcient optimality conditions of
first and second order are analysed. Special attention is paid on the effect of
the choice of the vector norm in the definition of the BV-seminorm for the
optimal primal and adjoined variables.
