WIAS Preprint No. 1700, (2012)

Second order sufficient optimality conditions for parabolic optimal control problems with pointwise state constraints


  • Krumbiegel, Klaus
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 35K20 35B65 47F05 49J20 49K20


  • Parabolic equation, maximal parabolic regularity, optimal control, sufficient optimality conditions


In this paper we study optimal control problems governed by semilinear parabolic equations where the spatial dimension is two or three. Moreover, we consider pointwise constraints on the control and on the state. We formulate first order necessary and second order sufficient optimality conditions. We make use of recent results regarding elliptic regularity and apply the concept of maximal parabolic regularity to the occurring partial differential equations.

Appeared in

  • SIAM J. Control Optim., 51 (2013) pp. 301--331.

Download Documents