We consider a Hamilton-Jacobi equation where the Hamiltonian is periodic in space and coercive and convex in momentum. Combining the representation formula from optimal control theory and a theorem of Alexander, originally proved in the context of first-passage percolation, we find a rate of homogenization which is within a log-factor of optimal and holds in all dimensions.

We consider the homogenization problem for fully nonlinear first order scalar partial differential equations of Hamilton-Jacobi type such as u(x) + H ( x, x ! , Du(x) ) = 0, x ∈ R , where ! is a… Expand

For a nonnegative subadditive function h on Z d , with limiting approximation g(x) = lim n h(nx)/n, it is of interest to obtain bounds on the discrepancy between g(x) and h(x), typically of order |x|… Expand

AbstractWe study the rate of convergence of $${u^\varepsilon}$$uε, as $${\varepsilon \to 0+}$$ε→0+, to u in periodic homogenization of Hamilton–Jacobi equations. Here, $${u^\varepsilon}$$uε and u are… Expand