We study the existence of optimal controls for problems governed by semilinear parabolic equations. The nonlinearities in the state equation need not be monotone and the data need not be regular. In particular, the control may be any bounded Radon measure. Our examples include problems with nonlinear boundary conditions and parabolic systems.
"Optimal control problems governed by semilinear parabolic equations with low regularity data." Adv. Differential Equations 11 (1) 1 - 33, 2006.