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Rate of convergence for periodic homogenization of convex Hamilton-Jacobi equations in one dimension
Let and be viscosity solutions of the oscillatory
Hamilton-Jacobi equation and its corresponding effective equation. Given
bounded, Lipschitz initial data, we present a simple proof to obtain the
optimal rate of convergence of as for a large class of convex
Hamiltonians in one dimension. This class includes the Hamiltonians
from classical mechanics with separable potential. The proof makes use of
optimal control theory and a quantitative version of the ergodic theorem for
periodic functions in dimension .Comment: 22 pages, typos corrected, references added, final accepted versio
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