Homogenization of the G-Equation: a metric approach

TL;DR

This paper simplifies the proof of homogenization results for the G-equation by introducing a metric approach that handles non-coercive Hamiltonians through multivalued dynamics and intrinsic distances.

Contribution

It provides a new, simpler method for homogenizing the G-equation without relying on coercivity, extending previous results with alternative techniques.

Findings

Homogenization results are recovered using a metric approach.

The method handles non-coercive Hamiltonians effectively.

A sequence of coercive Hamiltonians approximates the original problem.

Abstract

The aim of the paper is to recover some results of Cardaliaguet-Nolen-Souganidis in \cite{CNS} and Xin-Yu in \cite{XY} about the homogenization of the G--equation, using different and simpler techniques. The main mathematical issue is the lack of coercivity of the Hamiltonians. In our approach we consider a multivalued dynamics without periodic invariants sets, a family of intrinsic distances and perform an approximation by a sequence of coercive Hamiltonians.