On smooth approximations in the Wasserstein space

In this paper we investigate the approximation of continuous functions on Wasserstein space by smooth functions, with smoothness meant in sense Lions differentiability. particular, case a Lipschitz function are able to construct sequence infinitely differentiable having same constant as original function. This solves an open problem raised [12]. For (resp. twice) continuously function, show that our also holds for first-order derivative second-order derivatives), therefore solving another