A near-optimal rate of periodic homogenization for convex Hamilton-Jacobi equations
arXiv:2110.09430 · doi:10.1007/s00205-022-01797-x
Abstract
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.
6 pages, comments welcome! (added references and updated introduction)