Random homogenization of coercive Hamilton-Jacobi equations in 1d

TL;DR

This paper proves the random homogenization of general coercive non-convex Hamilton-Jacobi equations in one dimension, extending previous results to more general Hamiltonians without separability.

Contribution

It extends the homogenization results to non-separable, coercive, non-convex Hamilton-Jacobi equations in 1D, broadening the class of equations understood.

Findings

Proves homogenization for non-convex Hamilton-Jacobi equations in 1D.

Extends previous results to non-separable Hamiltonians.

Applicable to a broader class of coercive Hamiltonians.

Abstract

In this paper, we will prove the random homogenization of general coercive non-convex Hamilton-Jacobi equations in one dimensional case. This extends the result of Armstrong, Tran and Yu when the Hamiltonian has a separable form $H(p,x,\omega)=H(p)+V(x,\omega)$ for any coercive $H(p)$.