TY - GEN A1 - de Los Reyes, Juan Carlos A1 - Merino, Pedro A1 - Rehberg, Joachim A1 - Tröltzsch, Fredi T1 - Optimality Conditions for State-Constrained PDE Control Problems with Time-Dependent Controls N2 - The paper deals with optimal control problems for semilinear elliptic and parabolic PDEs subject to pointwise state constraints. The main issue is that the controls are taken from a restricted control space. In the parabolic case, they are vector-valued functions of the time, while they are vectors in elliptic problems. Under natural assumptions, first- and second-order sufficient optimality conditions are derived. The main result is the extension of second-order sufficient conditions to semilinear parabolic equations in domains of arbitrary dimension. In the elliptic case, the problems can be handled by known results of semi-infinite optimization. Here, different examples are discussed that exhibit different forms of active sets and where second-order sufficient conditions are satisfied at the optimal solution. Y1 - 2008 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/470 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4701 ER -