Homogenization on arbitrary manifolds. Proof with test functions

TL;DR

This paper proves the homogenization of Hamilton-Jacobi equations on any compact manifold using Evans' method, extending previous results to more general geometric settings.

Contribution

It introduces a proof of homogenization on arbitrary manifolds, broadening the applicability of existing techniques to complex geometric contexts.

Findings

Homogenization established on arbitrary compact manifolds.

Extension of Evans' test function method to new settings.

Framework applicable to diverse geometric structures.

Abstract

We proof the homogenization of the Hamilton-Jacobi equation on arbitrary compact manifolds using Evans perturbed test function method.