A projection exposure apparatus for semiconductor lithography has a connecting element for connecting a component of the apparatus to a supporting cooling structure of the apparatus. The connecting element has a receiving region for receiving the component, and the connecting element has a foot region for connecting the connecting element to the supporting cooling structure. At least one joint is arranged between the receiving and foot regions, and at least one heat conducting element is arranged between the receiving and foot regions. The heat conducting element is soft in the actuation direction of the joint and has a stiffness perpendicularly to the actuation direction of the joint that is at least twice as large as in the actuation direction of the joint.