Stochastic Time-Periodic Tonelli Lagrangian on Compact Manifold

TL;DR

This paper investigates stochastic time-periodic Tonelli Lagrangians on compact manifolds, establishing the stochastic Mane Critical Value, proving the existence of stochastic Weak KAM solutions, and surveying global minimizers.

Contribution

It introduces the concept of stochastic Mane Critical Value and proves the existence of stochastic Weak KAM solutions for the Hamilton-Jacobi equation on compact manifolds.

Findings

Existence of stochastic Weak KAM solutions

Identification of stochastic Mane Critical Value

Survey of global minimizers

Abstract

In this paper, we study a class of time-periodic stochastic Tonelli Lagrangians on compact manifolds. Precisely, we discuss the stochastic Mane Critical Value, prove the existence of stochastic Weak KAM solutions of the related Hamilton-Jacobi equation. Furthermore, we survey the global minimizer.