Lipschitz stability of solutions to parametric optimal control problems for parabolic equations

Abstract

A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, sufficient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L∞-norm. It is shown that these conditions are also necessary, provided that the dependence of data on the parameter is sufficiently strong. © Heldermann Verlag.