A SMOOTH VARIATIONAL PRINCIPLE ON WASSERSTEIN SPACE

In this note, we provide a smooth variational principle on Wasser-stein 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.

Automated summary

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