# Smoothing properties of McKean-Vlasov SDEs

## TL;DR

This paper develops integration by parts formulas for McKean-Vlasov SDEs with elliptic coefficients, enabling the analysis of derivatives and solutions to related PDEs with irregular terminal conditions.

## Contribution

It introduces new integration by parts formulas on Wiener space for McKean-Vlasov SDEs, addressing derivatives with respect to variables and measures, and provides bounds for solution densities.

## Key findings

- Established integration by parts formulas for McKean-Vlasov SDEs
- Proved existence of classical solutions to related PDEs with irregular terminal conditions
- Derived bounds for derivatives of solution densities

## Abstract

In this article, we develop integration by parts formulae on Wiener space for solutions of SDEs with general McKean-Vlasov interaction and uniformly elliptic coefficients. These integration by parts formulae hold both for derivatives with respect to a real variable and derivatives with respect to a measure understood in the sense of Lions. They allows us to prove the existence of a classical solution to a related PDE with irregular terminal condition. We also develop bounds for the derivatives of the density of the solutions of McKean-Vlasov SDEs.