Non-linear Stegall's lemma and general Hamilton-Jacobi-Bellman equations on Wasserstein spaces

Charles Bertucci; Pierre-Louis Lions

Non-linear Stegall's lemma and general Hamilton-Jacobi-Bellman equations on Wasserstein spaces

Analysis of PDEs 2026-06-30 v1 Functional Analysis

Authors: Charles Bertucci , Pierre-Louis Lions

Abstract

We present a comparison principle for unbounded viscosity solutions to Hamilton-Jacobi equations on Wasserstein spaces of probability measures over $R^d$ . In addition to the use of standard techniques of viscosity solutions, our approach requires a key extension on Wasserstein spaces of a result of perturbed optimization on Banach spaces due to Stegall.

Keywords

Hamilton-Jacobi equations Wasserstein spaces viscosity solutions comparison principle Stegall's lemma perturbed optimization

Cite

@article{arxiv.2606.31297,
  title  = {Non-linear Stegall's lemma and general Hamilton-Jacobi-Bellman equations on Wasserstein spaces},
  author = {Charles Bertucci and Pierre-Louis Lions},
  journal= {arXiv preprint arXiv:2606.31297},
  year   = {2026}
}