Lipschitz stability of solutions of linear-quadratic parabolic control problems with respect to perturbations

We consider a class of control problems governed by a linear parabolic init ial-boundary value problem with linear-quadratic objective and pointwise co nstraints on the control. The control system is subject to different types of perturbations. They appear in the linear part of the objective functiona l, in the right hand side of the equation, in its boundary condition, and i n the initial value. Employing results on parabolic regularity in the whole scale of L-P-spaces the known Lipschitz stability in the L-2-norm is stren gthened to the supremum-norm. AMS (MOS) subject classification: 49K20, 49K4 0.