Stochastic homogenization of nondegenerate viscous HJ equations in 1d

TL;DR

This paper establishes homogenization results for nondegenerate viscous Hamilton-Jacobi equations in one dimension within stationary ergodic environments, handling superlinear, nonconvex Hamiltonians of broad types.

Contribution

It proves homogenization for a class of viscous HJ equations with superlinear, nonconvex Hamiltonians in 1D, extending previous results to more general settings.

Findings

Homogenization proven for 1D viscous HJ equations in ergodic environments.

Handles superlinear, nonconvex Hamiltonians of general type.

Key theorem (4.2) crucial for the proof, previously appeared in arXiv preprint.

Abstract

We prove homogenization for a nondegenerate viscous Hamilton-Jacobi equation in dimension one in stationary ergodic environments with a superlinear (nonconvex) Hamiltonian of fairly general type. The version of the paper herein posted is identical to the one submitted to the journal *** for publication on the 26th of February, 2024. One of the crucial idea for the proof corresponds to Theorem 4.2. This theorem, together with its proof, already appeared, in essential identical form, in the ArXiv e-print 2306.12145, version 1 (posted on the 21st of June 2023), see Theorem 4.5 therein.