paper

A smooth variational principle on Wasserstein space

arXiv:2209.15028

Abstract

In this note, we provide a smooth variational principle on Wasserstein space by constructing a smooth gauge-type function using the sliced Wasserstein distance. This function is a crucial tool for optimization problems and in viscosity theory of PDEs on Wasserstein space.

Keywords: Smooth variational principle, sliced Wasserstein distance, optimal transport