Extension of Lipschitz functions

AbstractA function satisfying a Lipschitz property on an arbitrary set S is extended to the whole space E preserving the Lipschitz condition. This extension is obtained by performing the infimal convolution of two functions associated with the data of the problem. Comparison results between the generalized gradient of the extended function and that of the given function are provided. In view of applications, problems dealing with optimization and approximation of the extended function are studied