  The paper studies generalized differentiability properties of the marginal
function of parametric optimal control problems of semilinear elliptic partial
differential equations. We establish upper estimates for the regular and the
limiting subgradients of the marginal function. With some additional
assumptions, we show that the solution map of the perturbed optimal control
problems has local upper H\"{o}lderian selections. This leads to a lower
estimate for the regular subdifferential of the marginal function.
