Boundary control of parabolic systems: Regularity of optimal solutions

Boundary control problems for the linear, parabolic equations and a quadratic performance index are considered. The controls are allowed to be in the space L2[OT;L2(Γ)], where Γ is a boundary. Exploiting the semigroup approach, it is shown that optimal control belongs to L2[OT;H1/2(Γ)] and, as a consequence, optimal trajectory belongs to L1[OT;H1(Ω)]. This result is obtained for two kinds of domains. The first are the domains with C∞-boundary and the second are the domains being the parallelepipeds. © 1978 Springer-Verlag New York, Inc