A projection exposure apparatus for semiconductor lithography includes at least one component, and a support device with at least one support actuator which acts on at least one support location of the component so that deformations of the component are reduced. The support device includes a control unit for triggering the at least one support actuator. The control unit is configured to trigger the support actuator in the event of a dynamic acceleration acting on the component. The disclosure also relates to a method for reducing deformations, resulting from dynamic accelerations, of a projection exposure apparatus for semiconductor lithography.