Under monotonicity, solutions to static contact Hamilton-Jacobi equations with periodicity ε converge uniformly at rate O(ε) to the solution of an effective homogenized equation identified via Mather measures.
Convergence of the solutions of the discounted Hamilton–Jacobi equation: Convergence of the discounted solutions.Inventiones mathematicae 206, 1 (2016), 29–55
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Quantitative homogenization for static contact Hamilton-Jacobi equations
Under monotonicity, solutions to static contact Hamilton-Jacobi equations with periodicity ε converge uniformly at rate O(ε) to the solution of an effective homogenized equation identified via Mather measures.