  Many physical phenomena, governed by partial differential equations (PDEs),
are second order in nature. This makes sense to pose the control on the second
order derivatives of the field solution, in addition to zero and first order
ones, to consistently control the underlaying process. However, this type of
control is nontrivial and to the best of our knowledge there is nigher a
theoretic nor a numeric work in this regard. The present work goals to do the
first quest in this regard, examining a problem of this type using a numerical
simulation.
  A distributed parameter identification problem includes the control
  on the diffusion coefficient of the Poisson equation and a functional
includes the state's curvature is considered. A heuristic regularization tool
is introduced to manage codimension-one singularities during the functional
analysis. Based on the duality principles, the approximate necessary optimality
conditions is found. The system of optimality conditions is solved using a
globalized projected gradient method. Numerical results, in two- and
three-dimensions, implied the possibility of posing control on the second order
derivatives and success of the presented numerical method.
