A New Type Distribution Dependent SDE for Singular Nonlinear PDE

TL;DR

This paper introduces a novel distribution-dependent SDE linked to singular nonlinear PDEs, exploring its well-posedness and regularity properties to advance understanding of such equations.

Contribution

It proposes a new class of distribution-dependent SDEs connected to singular nonlinear PDEs, establishing their well-posedness and regularity results.

Findings

Established correspondence between the new SDE and singular nonlinear PDEs

Proved well-posedness of the proposed SDE

Analyzed regularity properties of solutions

Abstract

We propose a new type SDE depending on the future distributions with all initial values, and establish the correspondence between this equation and the associated singular nonlinear PDE. Well-posedness and regularities are investigated.